I decided to look this up and found thatthere is an issue. The issue is closed but it is not possible to simply runbrew updatebecause you will still get the same error.
So here is what you need to do:
cd /usr/local/Library
git pull origin master
In case you have changes in the directory (/usr/local/Library), the git pull will throw an error. In that case, you'll have to fetch the master branch and set it forcibly as master:
git fetch --all
git reset --hard origin/master
This will upgrade your homebrew and you can use brew again.
If you installed Homebrew as a non-root user, you'll need tocdto/Users/yourusername/homebrew/Libraryinstead of/usr/local/Library.