He was retconned at some point to be the son of a cosmonaut. I forget how he gets his krypton powers. It's all in his wiki:
The third attempt to bring Zod to Modern Age comics was the "Russian" Zod, a Zod of human origin whose origin story was connected to Superman's. This General Zod is a Russian who was affected before his birth by Kryptonite radiation, since he was the son of two cosmonauts whose ship was too close to Kal-El's rocketship. This Zod is unnaturally weak under a yellow sun, but superpowered under a red sun (the opposite of Superman).