I happened to try this so I could see the list of files first:
git status | grep "modified:" | awk '{print "git add " $2}' > file.sh
cat ./file.sh
execute:
chmod a+x file.sh
./file.sh
Edit: (see comments) This could be achieved in one step:
git status | grep "modified:" | awk '{print $2}' | xargs git add && git status