No food for a week wont kill the fish, they will be pretty hungry by day 7, but they will be OK.
Alternativly just cut down on the food for a while. 1/2 portions every 2nd day will do no harm either. The idea is to reduce the nutrients in the water, that cuts down the food for the algae/bacteria/diatoms that are making the water cloudy.
Other option would be a small UV filter, the UV light kills the micro organisms and will keep the water much clearer.
Sometimes water just goes cloudy in spite of everything seeming to be right.