As mentioned by @bentolo, you can manually delete the files it is complaining about, switch branches, and then manually add them back. But I personally prefer to stay "within git".
The best way to do this is to convert the stash to a branch. Once it is a branch you can work normally in git using the normal branch-related techniques/tools you know and love. This is actually a useful general technique for working with stashes even when you don't have the listed error. It works well because a stash really is a commit under the covers (see PS).
Converting a stash to a branch
The following creates a branch based on the HEAD when the stash was created and then applies the stash (it does not commit it).
git stash branch STASHBRANCH
Working with the "stash branch"
What you do next depends on the relationship between the stash and where your target branch (which I will call ORIGINALBRANCH) is now.
Option 1 - Rebase stash branch normally (lots of changes since stash)
If you have done a lot of changes in your ORIGINALBRANCH, then you are probably best treating STASHBRANCH like any local branch. Commit your changes in STASHBRANCH, rebase it on ORIGINALBRANCH, then switch to ORIGINALBRANCH and rebase/merge the STASHBRANCH changes over it. If there are conflicts then handle them normally (one of the advantages of this approach is you can see and resolve conflicts).
Option 2 - Reset original branch to match stash (limited changes since stash)
If you just stashed while keeping some staged changes, then committed, and all you want to do is get the additional changes that where not staged when you stashed you can do the following. It will switch back to your original branch and index without changing your working copy. The end result will be your additional stash changes in your working copy.
git symbolic-ref HEAD refs/heads/ORIGINALBRANCH
git reset
Background
Stashes are commits likes branches/tags (not patches)
PS, It is tempting to think of a stash as a patch (just like it is tempting to think of a commit as a patch), but a stash is actually a commit against the HEAD when it was created. When you apply/pop you are doing something similar to cherry-picking it into your current branch. Keep in mind that branches and tags are really just references to commits, so in many ways stashes, branches, and tags are just different ways of pointing at a commit (and its history).
Sometimes needed even when you haven't made working directory changes
PPS, You may need this technique after just using stash with --patch and/or --include-untracked. Even without changing working directories those options can sometimes create a stash you can't just apply back. I must admit don’t fully understand why. See http://git.661346.n2.nabble.com/stash-refuses-to-pop-td7453780.html for some discussion.
git checkout stash -- .
) – Poucher