diff --git a/Library/Homebrew/dev-cmd/extract.rb b/Library/Homebrew/dev-cmd/extract.rb
index dca97bc7ec..fb8aa976a6 100644
--- a/Library/Homebrew/dev-cmd/extract.rb
+++ b/Library/Homebrew/dev-cmd/extract.rb
@@ -81,7 +81,8 @@ module Homebrew
 
         Look through repository history to find the most recent version of <formula> and
         create a copy in <tap>`/Formula/`<formula>`@`<version>`.rb`. If the tap is not
-        installed yet, attempt to install/clone the tap before continuing.
+        installed yet, attempt to install/clone the tap before continuing. To extract
+        a <formula> from a tap that is not homebrew/core use <user>/<repo>/<formula>.
       EOS
 
       flag "--version=",
@@ -97,47 +98,70 @@ module Homebrew
     # Expect exactly two named arguments: formula and tap
     raise UsageError if ARGV.named.length != 2
 
+    if ARGV.named.first !~ HOMEBREW_TAP_FORMULA_REGEX
+      name = ARGV.named.first.downcase
+      source_tap = CoreTap.instance
+    else
+      name = Regexp.last_match(3).downcase
+      source_tap = Tap.fetch(Regexp.last_match(1), Regexp.last_match(2))
+      raise TapFormulaUnavailableError.new(source_tap, name) unless source_tap.installed?
+    end
+
     destination_tap = Tap.fetch(ARGV.named.second)
     odie "Cannot extract formula to homebrew/core!" if destination_tap.core_tap?
+    odie "Cannot extract formula to the same tap!" if destination_tap == source_tap
     destination_tap.install unless destination_tap.installed?
 
-    name = ARGV.named.first.downcase
-    repo = CoreTap.instance.path
-    # Formulae can technically live in "<repo>/<formula>.rb" or
-    # "<repo>/Formula/<formula>.rb", but explicitly use the latter for now
-    # since that is how the core tap is structured.
-    file = repo/"Formula/#{name}.rb"
+    repo = source_tap.path
+    pattern = if source_tap.core_tap?
+      [repo/"Formula/#{name}.rb"]
+    else
+      # A formula can technically live in the root directory of a tap or in any of its subdirectories
+      [repo/"#{name}.rb", repo/"**/#{name}.rb"]
+    end
 
     if args.version
       ohai "Searching repository history"
       version = args.version
       rev = "HEAD"
       test_formula = nil
+      result = ""
       loop do
-        loop do
-          rev = Git.last_revision_commit_of_file(repo, file, before_commit: "#{rev}~1")
-          break if rev.empty?
-          break unless Git.last_revision_of_file(repo, file, before_commit: rev).empty?
+        rev, (path,) = Git.last_revision_commit_of_files(repo, pattern, before_commit: "#{rev}~1")
+        odie "Could not find #{name}! The formula or version may not have existed." if rev.nil?
 
+        file = repo/path
+        result = Git.last_revision_of_file(repo, file, before_commit: rev)
+        if result.empty?
           ohai "Skipping revision #{rev} - file is empty at this revision" if ARGV.debug?
+          next
         end
+
         test_formula = formula_at_revision(repo, name, file, rev)
         break if test_formula.nil? || test_formula.version == version
 
         ohai "Trying #{test_formula.version} from revision #{rev} against desired #{version}" if ARGV.debug?
       end
       odie "Could not find #{name}! The formula or version may not have existed." if test_formula.nil?
-      result = Git.last_revision_of_file(repo, file, before_commit: rev)
-    elsif File.exist?(file)
-      rev = "HEAD"
-      version = Formulary.factory(file).version
-      result = File.read(file)
     else
-      ohai "Searching repository history"
-      rev = Git.last_revision_commit_of_file(repo, file)
-      version = formula_at_revision(repo, name, file, rev).version
-      odie "Could not find #{name}! The formula or version may not have existed." if rev.empty?
-      result = Git.last_revision_of_file(repo, file)
+      # Search in the root directory of <repo> as well as recursively in all of its subdirectories
+      files = Dir[repo/"{,**/}"].map do |dir|
+        Pathname.glob(["#{dir}/#{name}.rb"]).find(&:file?)
+      end.compact
+
+      if files.empty?
+        ohai "Searching repository history"
+        rev, (path,) = Git.last_revision_commit_of_files(repo, pattern)
+        odie "Could not find #{name}! The formula or version may not have existed." if rev.nil?
+        file = repo/path
+        version = formula_at_revision(repo, name, file, rev).version
+        result = Git.last_revision_of_file(repo, file)
+      else
+        file = files.first.realpath
+        rev = "HEAD"
+        version = Formulary.factory(file).version
+        result = File.read(file)
+      end
     end
 
     # The class name has to be renamed to match the new filename,
diff --git a/Library/Homebrew/utils/git.rb b/Library/Homebrew/utils/git.rb
index e0bb176fed..875b07dc13 100644
--- a/Library/Homebrew/utils/git.rb
+++ b/Library/Homebrew/utils/git.rb
@@ -4,7 +4,11 @@ module Git
   module_function
 
   def last_revision_commit_of_file(repo, file, before_commit: nil)
-    args = [before_commit.nil? ? "--skip=1" : before_commit.split("..").first]
+    args = if before_commit.nil?
+      ["--skip=1"]
+    else
+      [before_commit.split("..").first]
+    end
 
     out, = Open3.capture3(
       HOMEBREW_SHIMS_PATH/"scm/git", "-C", repo,
@@ -14,6 +18,28 @@ module Git
     out.chomp
   end
 
+  def last_revision_commit_of_files(repo, files, before_commit: nil)
+    args = if before_commit.nil?
+      ["--skip=1"]
+    else
+      [before_commit.split("..").first]
+    end
+
+    # git log output format:
+    #   <commit_hash>
+    #   <file_path1>
+    #   <file_path2>
+    #   ...
+    # return [<commit_hash>, [file_path1, file_path2, ...]]
+    out, = Open3.capture3(
+      HOMEBREW_SHIMS_PATH/"scm/git", "-C", repo, "log",
+      "--pretty=format:%h", "--abbrev=7", "--max-count=1",
+      "--diff-filter=d", "--name-only", *args, "--", *files
+    )
+    rev, *paths = out.chomp.split(/\n/).reject(&:empty?)
+    [rev, paths]
+  end
+
   def last_revision_of_file(repo, file, before_commit: nil)
     relative_file = Pathname(file).relative_path_from(repo)
 
diff --git a/docs/Manpage.md b/docs/Manpage.md
index 948500a123..a47c0784ef 100644
--- a/docs/Manpage.md
+++ b/docs/Manpage.md
@@ -782,7 +782,8 @@ Homebrew repository for editing if no *`formula`* is provided.
 
 Look through repository history to find the most recent version of *`formula`* and
 create a copy in *`tap`*`/Formula/`*`formula`*`@`*`version`*`.rb`. If the tap is not
-installed yet, attempt to install/clone the tap before continuing.
+installed yet, attempt to install/clone the tap before continuing. To extract a
+*`formula`* from a tap that is not homebrew/core use *`user`*/*`repo`*/*`formula`*.
 
 * `--version`:
   Extract the provided *`version`* of *`formula`* instead of the most recent.
diff --git a/manpages/brew.1 b/manpages/brew.1
index 8675833751..0816a4624f 100644
--- a/manpages/brew.1
+++ b/manpages/brew.1
@@ -981,7 +981,7 @@ Generate the new formula in the provided tap, specified as \fIuser\fR\fB/\fR\fIr
 Open a formula in the editor set by \fBEDITOR\fR or \fBHOMEBREW_EDITOR\fR, or open the Homebrew repository for editing if no \fIformula\fR is provided\.
 .
 .SS "\fBextract\fR [\fIoptions\fR] \fIformula\fR \fItap\fR"
-Look through repository history to find the most recent version of \fIformula\fR and create a copy in \fItap\fR\fB/Formula/\fR\fIformula\fR\fB@\fR\fIversion\fR\fB\.rb\fR\. If the tap is not installed yet, attempt to install/clone the tap before continuing\.
+Look through repository history to find the most recent version of \fIformula\fR and create a copy in \fItap\fR\fB/Formula/\fR\fIformula\fR\fB@\fR\fIversion\fR\fB\.rb\fR\. If the tap is not installed yet, attempt to install/clone the tap before continuing\. To extract a \fIformula\fR from a tap that is not homebrew/core use \fIuser\fR/\fIrepo\fR/\fIformula\fR\.
 .
 .TP
 \fB\-\-version\fR