The former Mr Universe and winner of dozens of bodybuilding titles, wants pupils of all ages to exercise for 30 to 60 minutes at least three times a week. Schools will be monitored for four weeks and the one with the highest proportion of children meeting the target will win a new fitness centre.
Eleven runners-up will get $1,000 (pound;507) for gym equipment.
The Terminator star told students: "It's not just to have a muscular body and to look studly when you go out there - it has also to do with your health, because so many people get sick as they get older."
It can only be hoped that California's students do not go too far in emulating the Governator's personal fitness regime. Mr Schwarzenegger has admitted to taking steroids before they became illegal and breaking into gyms in his native Austria as a teenager so he could weightlift at weekends.