With the advent of the space industry, hybrid satellite-terrestrial cooperative systems (HSTCSs) have drawn significant attention due to their prominent advantages. Besides, a novel modulation technique called spatial modulation (SM), which uses transmit antenna indices as additional information conveying source, is another technology envisioned to be used for next-generation communication systems. In this article, we propose to use SM in an HSTCS scheme consisting of a satellite, multiple terrestrial relays with multiple-input and multiple-output configuration, and a destination node equipped with multiple antennas on the ground. We derive a union bound for the symbol error probability in a fairly exact form and diversity order to shed light on the significant system parameters on the performance. Our theoretical results are validated through Monte Carlo simulations, and it is shown that using the SM technique provides a better error performance in the considered HSTCS system when compared to vertical Bell Laboratories layered space-time and space-time Alamouti codes.