This paper presents an analysis of frequency-offset estimation in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. Tracking of the frequency offset between a transmitter and a receiver is often aided by transmitting pilots embedded in the data payload of a packet. The extension to multiple-antenna OFDM systems means that spatial beamforming will occur when transmitting pilots from all antennas simultaneously, which can reduce the robustness of frequency-offset estimation. This paper presents a thorough analysis of the spatial beamforming problem, and shows how the spatial correlation of the MIMO channel impacts performance. Simulation results are presented for both synthetic and measured channels, which agree well with the theoretical results