This paper presents a novel approach to address the problem of intercepting non-cooperative targets with multiple satellites in Earth orbit. The multi-satellite interception problem is formulated as a multi-player pursuit–evasion game that explicitly accounts for stochastic disturbances and control constraints. By combining differential game theory with stochastic optimization techniques, the paper derives optimal interception trajectories that ensure safety and performance under modeling uncertainties. A linear exponential quadratic cost functional is established, and corresponding Nash equilibrium strategies are obtained to determine the optimal control laws. Numerical simulations validate the effectiveness and robustness of the proposed approach in achieving reliable interception performance.