This paper proposes a novel method for channel estimation in a single-carrier MIMO system with frequency-domain equalization/detection. To this end, we construct novel short MIMO training sequences that have a constant envelope in the time domain to preclude the peak-to-mean power problem encountered in many systems that utilize the frequency domain for data recovery. Simultaneously, the spectrum in the frequency domain is flat except for a grid of nulls for predefined frequency tones. Such construction allows us to interpolate over nulled tones to recover the full set of MIMO channel state information (CSI). The interpolation is performed by a specially crafted algorithm which iteratively reconstructs the full CSI by a series of FFT and IFFT operations. This algorithm is extremely bandwidth efficient in that the total training overhead required to obtain full CSI is just one block period.