This paper studies the problem of linear precoding for multiple-input multiple-output (MIMO) communication channels employing finite-alphabet signaling. Existing solutions typically suffer from high computational complexity due to costly computations of the constellation-constrained mutual information. In contrast to existing works, this paper takes a different path of tackling the MIMO precoding problem. Namely, a data-driven approach, based on deep learning, is proposed. In the offline training phase, a deep neural network learns the optimal solution on a set of MIMO channel matrices. This allows the reduction of the computational complexity of the precoder optimization in the online inference phase. Numerical results demonstrate the efficiency of the proposed solution vis-à-vis existing precoding algorithms in terms of significantly reduced complexity and close-to-optimal performance.