I had ganglion cyst wrist surgery 3 weeks ago, how much longer will I have pain when I move my wrist. I hurts when I take splint off and move it.

Most pain. Dissipates in a few weeks. Though the exact size, location of the cysts and other issues in the wrist such as arthritis, underlying ligament and capsular issues and even how and why the ganglion was removed can play a role. Talk to yiour surgeon regarding your scenario. Though rare, there are times when therapy is needed to get moving. And a splint while it helps may need to be weaned sooner.
Let me explain. It take about 6-8 weeks to fully recover from this surgery.