This paper proposes and analyzes a mmWave sparse channel estimation technique for OFDM systems that uses the Orthogonal Matching Pursuit (OMP) algorithm. This greedy algorithm retrieves one additional multipath component (MPC) per iteration until a stop condition is met. We obtain an analytical approximation for the OMP estimation error variance that grows with the number of retrieved MPCs (iterations). The OMP channel estimator error variance outperforms a classic maximum-likelihood (ML) non-sparse channel estimator by a factor of approximately $2\hat{L}/M$ where $\hat{L}$ is the number of retrieved MPCs (iterations) and $M$ the number of taps of the Discrete Equivalent Channel. When the MPC amplitude distribution is heavy-tailed, the channel power is concentrated in a subset of dominant MPCs. In this case OMP performs fewer iterations as it retrieves only these dominant large MPCs. Hence for this MPC amplitude distribution the estimation error advantage of OMP over ML is improved. In particular, for channels with MPCs that have lognormally-distributed amplitudes, the OMP estimator recovers approximately 5-15 dominant MPCs in typical mmWave channels, with 15-45 weak MPCs that remain undetected.