The problem of robust training sequence design for the purpose of multiple-input multiple-output (MIMO) channel estimation is considered. In particular, we aim to minimize the worst-case mean squared error of the channel estimates which is formulated as a minimax optimization problem. This problem is addressed efficiently using an extended barrier method under the general assumption of an arbitrary compact convex uncertainty set. Moreover, assuming a Kronecker MIMO channel and a unitarily invariant uncertainty set, the robust design problem is diagonalized which significantly lowers the dimensionality of the optimization problem. We provide numerical examples to illustrate the performance of the proposed design.