Various emerging applications in sixth-generation (6G) wireless demand a seamless integration of communication and sensing services, driving the development of integrated sensing and communication (ISAC) systems. Using a common waveform for both functions introduces additional security challenges, as information-bearing signals are vulnerable to eavesdropping. While a variety of secure beamforming designs are proposed in the literature for metasurface-enabled ISAC systems with single-antenna users and eavesdroppers, optimal designs for multi-antenna scenarios remain unexplored. This paper addresses this gap by studying a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-enabled multi-user multiple-input multiple-output (MU-MIMO) ISAC system and proposing an optimal beamforming design to maximize the sum secrecy rate while ensuring sensing quality for multiple targets. An alternating-optimization based iterative solution is developed to tackle the non-convex optimization problem. The presented analysis confirms that the computational complexity of the proposed algorithm grows linearly with the number of metasurface elements. Our numerical results show the benefit of using STAR-RIS to increase the sum secrecy rate of the MU-MIMO ISAC system compared to its corresponding conventional RIS (cRIS)-enabled and w/o RIS systems.