Like the others said, if the branch you are looking for isn’t local to the repository on which you are blaming this commit (e.g. a branch only in the personal repo of a distant developer), you are screwed.
But assuming that sought-after branch is something you can see, and that of course you have the commit’s hash, say d590f2..., a partial answer is that you can do :
$ git branch --contains d590f2
tests
* master
Then, just to confirm you have the culprit:
$ git rev-list tests | grep d590f2
Of course, if d590f2 has been merged in more than one branch, you will have to be more subtle than this.