Photon counting is a promising solution to detecting low-power optical signals for ultraviolet (UV) communications in the forthcoming sixth-generation (6G) network. Different from the conventional additive white Gaussian noise (AWGN) model, the discrete signal-dependent Poisson shot noise poses challenges to the signal processing of photon-counting systems. In this paper, a joint design of precoder and equalizer is proposed for photon-counting multiple-input multiple-output (PhC-MIMO) UV systems. To circumvent the impasse arising from the signal-dependent shot noise, we propose an alternating optimization algorithm based on the minimum mean squared error (MMSE) criterion. The algorithm decomposes the joint design into convex subproblems solved in an alternating manner, and guarantees at least a stationary point solution. Numerical results corroborate that the proposed system exhibits robustness to turbulence fading and offers high throughput while mitigating the adverse effect of background radiation noise. Specifically, the 32 × 8 system can achieve a bit error rate (BER) of 10-5 at the signal energy of -154.0 dBJ per bit under strong Gamma-Gamma turbulence with the scintillation index (S.I.) of 3.