They didn't have the range (200mi) to be effective over the vast distances on the Eastern Front. They also needed large convoys and assemblies to fire from, filled with volatile chemicals and some of their top scientists, not to mention secrets of design and manufacture. This is fine at Peenemunde, where you're in range of the enemy but out of their reach. No danger that the British army's going to suddenly come around the corner and capture some of your best secrets. But in the East, Russia could have easier access to the base. Then they'd have the rockets. And they'd definitely use them against their inventors. By the time the V2 came into service, things were looking bad in the East. Wouldn't have been worth the risk.

Additionally, the V weapons weren't very effective. They were tools of terror, not something of true heavy military use. They were "just" a self-propelled 2,000lb bomb. Drop a few in London, and maybe panic would tie up the RAF and government for an evening and eventually civilians would force Churchill to negotiate peace, but drop a few in the East and you'd kill maybe a hundred or so out of hundreds of thousands of soldiers. You certainly didn't have the accuracy to do targeted damage (otherwise Downing St. would have been targeted in London).