Recently, coprime arrays have attracted lots of interest due to their ability of providing enhanced degrees-of-freedom and reduced mutual coupling effect compared to conventional uniform linear arrays. Benefitting from these excellent properties, coprime multiple-input multiple-output (MIMO) radar has been recently suggested for improving parameter identifiability and target detection. In this paper, we address the problem of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation of coherent targets in coprime MIMO radar. First of all, we establish an extended virtual uniform rectangular array (URA) by performing array interpolation on the transmit and receive arrays of coprime MIMO radar. Subsequently, we derive a low-rank block Hankel matrix that is constructed using the correlation information of the virtual URA expected outputs, and utilize the matched filter outputs to recover the block Hankel matrix by solving a low-rank structured matrix completion problem. Finally, we estimate the DODs and DOAs of coherent targets by applying the modified matrix pencil method on the recovered low-rank matrix. We also derive the Cramér-Rao bounds with closed-form expressions for DOD and DOA estimation of coherent targets using coprime MIMO radar. The proposed algorithm can identify multiple coherent targets and achieve parameter automatic pairing. Numerical results demonstrate the superiority of the proposed algorithm over several existing approaches when handling coherent targets.