In this paper, we study the problem of joint active and passive beamforming for intelligent reflecting surface (IRS)-assisted massive MIMO systems, where multiple IRSs equipped with a large number of passive elements are deployed to assist a base station (BS) to simultaneously serve a small number of single-antenna users in the same time-frequency resource. Our objective is to maximize the minimum signal to interference plus noise (SINR) at users by jointly optimizing the transmit precoding vector at the BS and phase shift parameters at IRSs. We show that an interesting automatic interference cancelation (AIC) property holds asymptotically as the number of passive elements approaches infinity, i.e., when an IRS is optimally tuned to serve a certain user, this IRS will become interference-free to other users. By utilizing this property, the max-min problem can be converted into an IRS-user association problem, where the objective is to determine which IRSs are assigned for each user. An exhaustive search scheme and a greedy search scheme are proposed to solve the IRS-user association problem. Our theoretical analysis reveals that our proposed solution attains an SINR that scales quadratically with the number of reflecting elements. Also, our theoretical result suggests that even with a moderate number of active antennas at the BS, a massive MIMO like gain can be achieved by increasing the number of passive reflecting elements, thus significantly reducing the energy consumption at the BS. Simulation results are provided to corroborate our theoretical results and to illustrate the effectiveness of our proposed solution.