Noise pollution from heat pumps (HPs) has been an emerging concern to their broader adoption, especially in densely populated areas. This paper explores a model predictive control (MPC) approach for climate control of buildings, aimed at minimizing the noise nuisance generated by HPs. By exploiting a piecewise linear approximation of HP noise patterns and assuming linear building thermal dynamics, the proposed design can be generalized to handle various HP acoustic patterns with mixed-integer linear programming (MILP). Additionally, two computationally efficient options for defining the noise cost function in the proposed MPC design are discussed. Numerical experiments on a high-fidelity building simulator are performed to demonstrate the viability and effectiveness of the proposed design. Simulation results show that minimizing the excess of HP noise over ambient noise is effective in mitigating the HP noise nuisance. Further, compared with the conventional MPC-based building climate control scheme, the proposed approach can effectively reduce the HP noise pollution with only a minor energy cost increase.