Wireless energy harvesting in millimeter wave (mmWave) cellular networks is attractive, thanks to the large antenna arrays and the anticipated dense deployment of these systems. The signal propagation at mmWave frequencies, however, shows peculiar propagation characteristics such as extreme sensitivity to building blockages. This work analyzes the energy harvesting performance at receivers powered by a mmWave cellular network. Leveraging tools from stochastic geometry, analytical expressions are derived to characterize the energy coverage probability at a typical receiver in terms of the cellular network density, the antenna geometry parameters, and the channel parameters. Results show that there typically exists an optimum transmit antenna beamwidth that maximizes the network-wide energy coverage probability for many operating scenarios. Simulation results further suggest that mmWave energy harvesting could provide a substantial performance boost compared to lower frequency solutions.