In millimeter wave (mmWave) communication systems with hybrid multiple-input multiple-output (MIMO) processors, it is often necessary to employ analog beam sweeping during pilot signal transmission/reception to increase the signal to noise ratio (SNR). In this paper, we develop a process, called the space-time (ST) alignment, for receiving pilot sequences for mmWave channel estimation from the signal received during beam sweeping. The spatial alignment removes the effect of beam sweeping on pilot arrival time (PATs). The process for locating the temporal windows on the received signal to obtain pilot-containing sequences for channel estimation is called the temporal alignment. Simulation results demonstrate that mmWave channels can be estimated successfully using the sequences obtained via the ST alignment.