As per my Answer here: How to remove a directory from git repository?
Steps to remove directory
git rm -r --cached FolderName
git commit -m "Removed folder from repository"
git push origin master
Steps to ignore that folder in next commits
To ignore that folder from next commits make one file in root named .gitignore and put that folders name into it. You can put as many as you want
.gitignore file will be look like this
/FolderName