An excellent tool I have used for similar purposes in the past (although it can do other things as well) is git-subtree. I recommend checking it out: https://github.com/apenwarr/git-subtree
That was my thought as well, but then I thought that the requirements might be different here. git-subtree would allow you to create a git repository (with history) from a directory in a pre-existing repository. You could them just 'git rm -r' the directory from the original repository, but I'm not sure if the requirements here are to completely remove the history of that directory from the original repository too (because git-subtree doesn't do that, to my knowledge).