Intelligent reflecting surface (IRS)-enabled communication systems provide higher system capacity and spectral efficiency by reflecting the incident signals from transmitters in a low-cost passive reflecting way. However, it poses new challenges in resource allocation due to surrounding interference and phase shift, especially when IRS is employed in heterogeneous networks (HetNets). In this paper, a joint power allocation and phase shift optimization problem is studied for the downlink IRS-enabled HetNet, in which the IRS is deployed to enhance the communications between small cell users (SCUs) and associated base station (BS). The signal-to-interference-plus-noise ratio (SINR) received at the SCU is maximized by jointly optimizing the transmit power of the small-cell BS and the phase shift of the IRS, subject to the constraints on the minimum SINR requirement of the macro-cell user (MCU) and the phase shift. Although the formulated problem is non-convex, we develop an optimal power allocation and the IRS’s passive array coefficient solution for the single-user scenario. For the multi-user scenario, we propose an iterative algorithm to maximize the total rates of SCUs for obtaining a suboptimal solution by an alternating iteration manner, where the sum of multiple-ratio fractional programming problem is converted into a convex semidefinite program (SDP) problem. Simulation results show that the proposed algorithm significantly improves the achieved transmission rates of SCUs compared to the case without the IRS.