Time-division multiplexed switching (TDMS)-based multiple-input multiple-output (MIMO) channel sounders are widely used for wireless channel measurements due to their effective costs. However, measurement noise such as phase noise in the local oscillators as well as additive white Gaussian noise (AWGN) can result in significant errors in channel capacity estimates. This study analyzes the impact of phase noise and AWGN on channel capacity in TDMS-based MIMO measurements, with a channel capacity estimator presented that reduces the impact of noise on both the spatial multiplexing gain and on the power gain. Simulations demonstrate that the estimator consistently obtains the true capacity for various MIMO channel scenarios, even if only a limited number of observations are available.