Even shorter:
git branch --contains tags/<tag>
(it works for any tree-ish reference)
If you can find which commit a tag refers to:
git rev-parse --verify tags/<tag>^{commit}
# or, shorter:
git rev-parse tags/<tag>~0
Then you can find which branch contain that commit.
git branch --contains <commit>
As commented below by user3356885, for the fetched branches (branches in remotes namespace)
git branch -a --contains tags/<tag>
git branch -a --contains <commit>
As noted in Pyr3z‘s answer, for each candidate tag listed above, you can add:
git log -1 --pretty='%D' TAG
That will show the branches associated to that tag.