git tag --merged <branch>
From the man page:
--[no-]merged <commit>
Only list tags whose tips are reachable, or not reachable if --no-merged is used, from the specified commit (HEAD if not specified).
I believe this option was added quite recently – it definitely wasn’t available back when the original question was posed and the above answers suggested. Since this thread is still the first hit in Google for the question I figured I’d throw it in for anyone who scrolls down to the bottom looking for an answer that involves less typing than the accepted answer (and for my own reference when I forget this answer again next week).