We consider a single-cell full-duplex (FD) network. In FD transmission, the downlink rate is degraded by the cochannel interference (CCI) from the active uplink transmission. In this letter, we study how utilizing reconfigurable intelligent surfaces (RIS) can mitigate the effects of the CCI. In a multiple-input-multiple-output (MIMO) network, we consider two scenarios for CCI cancellation. In the first scenario, we assume that both the RIS-base station uplink and downlink direct links suffer from deep fading, i.e., they do not exist. In that case, the CCI minimization problem will be cast as an unconstrained manifold optimization problem. In the second scenario, we assume that the RIS-base station uplink and downlink direct links exist and the RIS controls all the network's links. In that case, the CCI minimization problem will be constrained by the uplink and the downlink channel gains, and accordingly, a penalty-based approach will be adopted to solve the CCI minimization problem. Our results show that utilizing the RIS can be very effective in minimizing the CCI and achieving a higher downlink rate than benchmark schemes.