They do sell solenoid pinch valves specifically for that purpose. I've noticed they're quite expensive, probably because of their typical medical or scientific application (other applications will usually just use a standard solenoid valve). You might be able to get a deal on surplus pinch valves if you get lucky on eBay. I think you may be limited to certain properties of tubing.
Possibly more fun/cheap would be to find a DIY solution. Solenoids are fairly cheap, you just need to get one with enough force and build the pinch parts. Even if you don't need a pump, the mechanisms you find in DIY peristaltic pumps could be adapted to work as a pinch valve if for some reason you found using a motor preferable to a solenoid.