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In this paper, a coarray tensor completion-based direction-of-arrival (DOA) estimation method is proposed for coprime planar array. To perform Nyquist-matched coarray signal processing, the completion of the coarray tensor corresponding to an augmented discontinuous virtual array is pursued. However, it is difficult to impose a low-rank regularization on the incomplete coarray tensor with slices of missing elements for its completion. To solve this problem, a structural tensorization approach is designed to reshape the incomplete coarray tensor into one with distributed missing elements. As such, a coarray tensor completion problem based on tensor nuclear norm minimization is formulated to complete these missing elements. By exploiting the filled virtual array obtained from the completed coarray tensor, a super-resolution DOA estimation can be achieved in closed-form.