The best option is to stage everything but this file, and tell stash to keep the index with git stash save --keep-index, thus stashing your unstaged file:
$ git add .
$ git reset thefiletostash
$ git stash save --keep-index
As Dan points out, thefiletostash is the only one to be reset by the stash, but it also stashes the other files, so it's not exactly what you want.
If you do not want to specify a message with your stashed changes, pass the filename after a double-dash.
$ git stash -- filename.ext
If it's an untracked/new file, you will have to stage it first.
However, if you do want to specify a message, use push.
git stash push -m "describe changes to filename.ext" filename.ext
Both methods work in git versions 2.13+
You can interactively stash single lines with git stash -p (analogous to git add -p).
It doesn't take a filename, but you could just skip other files with d until you reached the file you want stashed and the stash all changes in there with a.
Just in case you actually mean 'discard changes' whenever you use 'git stash' (and don't really use git stash to stash it temporarily), in that case you can use
git checkout -- <file>
Note that git stash is just a quicker and simple alternative to branching and doing stuff.
Source: Stackoverflow.com