This looks like powdery mildew on the foliage, a fungal disease. Warm moist weather favors this disease.
The best recommendation is to plant powdery mildew resistant varieties. See the list from Cornell http://vegetablemdonline.ppath.cornell.edu/Tables/Cucurbit_zucchini%20table2016.pdf
This season you could try a horticultural oil labeled for powdery mildew control. Do not spray in hot weather. At the end of the season, prune out and dispose of any plant material that had symptoms, to help cut down on overwintering spores.