Reconfigurable intelligent surfaces (RISs) are regarded as an emerging technology for the next generation of wireless communications. In this paper, we consider a multiple-input multiple-output network where each base station serves a user equipment with the aid of an RIS equipped with N reconfigurable elements. We characterize the interference at one user equipment that is caused by the signal emitted by its non-serving (interfering) RIS. By assuming Rayleigh fading channels, we study the corresponding interference-to-noise- ratio (INR) under the assumption of large values of N, and we prove that the INR is the product of a Chi-Square random variable (RV) and an RV that is approximated with a Gamma distribution. In addition, we prove that the amount of fading of the INR is equal to one in the large N regime.