As has been said elsewhere, the answer is to git add the file. e.g.:
git add path/to/untracked-file
git stash
However, the question is also raised in another answer: What if you don't really want to add the file? Well, as far as I can tell, you have to. And the following will NOT work:
git add -N path/to/untracked/file # note: -N is short for --intent-to-add
git stash
this will fail, as follows:
path/to/untracked-file: not added yet
fatal: git-write-tree: error building trees
Cannot save the current index state
So, what can you do? Well, you have to truly add the file, however, you can effectively un-add it later, with git rm --cached:
git add path/to/untracked-file
git stash save "don't forget to un-add path/to/untracked-file" # stash w/reminder
# do some other work
git stash list
# shows:
# stash@{0}: On master: don't forget to un-add path/to/untracked-file
git stash pop # or apply instead of pop, to keep the stash available
git rm --cached path/to/untracked-file
And then you can continue working, in the same state as you were in before the git add (namely with an untracked file called path/to/untracked-file; plus any other changes you might have had to tracked files).
Another possibility for a workflow on this would be something like:
git ls-files -o > files-to-untrack
git add `cat files-to-untrack` # note: files-to-untrack will be listed, itself!
git stash
# do some work
git stash pop
git rm --cached `cat files-to-untrack`
rm files-to-untrack
[Note: As mentioned in a comment from @mancocapac, you may wish to add --exclude-standard to the git ls-files command (so, git ls-files -o --exclude-standard).]
... which could also be easily scripted -- even aliases would do (presented in zsh syntax; adjust as needed) [also, I shortened the filename so it all fits on the screen without scrolling in this answer; feel free to substitute an alternate filename of your choosing]:
alias stashall='git ls-files -o > .gftu; git add `cat .gftu`; git stash'
alias unstashall='git stash pop; git rm --cached `cat .gftu`; rm .gftu'
Note that the latter might be better as a shell script or function, to allow parameters to be supplied to git stash, in case you don't want pop but apply, and/or want to be able to specify a specific stash, rather than just taking the top one. Perhaps this (instead of the second alias, above) [whitespace stripped to fit without scrolling; re-add for increased legibility]:
function unstashall(){git stash "${@:-pop}";git rm --cached `cat .gftu`;rm .gftu}
Note: In this form, you need to supply an action argument as well as the identifier if you're going to supply a stash identifier, e.g. unstashall apply stash@{1} or unstashall pop stash@{1}
Which of course you'd put in your .zshrc or equivalent to make exist long-term.
Hopefully this answer is helpful to someone, putting everything together all in one answer.