Plugging a side pocket mandrel using a swelling plug. A system for plugging a port in a side pocket of a mandrel in a subterranean well includes a plugging device installed in the side pocket of the mandrel, the plugging device including a swellable seal material, whereby the seal material swells at least after installation of the plugging device in the side pocket to thereby prevent fluid transfer through the port. A method of plugging a port in a side pocket of a mandrel in a subterranean well includes the steps of: providing the plugging device with a swellable seal material; installing the plugging device in the side pocket; and the seal material swelling in the side pocket, thereby preventing fluid transfer through the port.