For the terrestrial planets of our solar system, Jupiter was an important influence: it sculpted the dynamical environment in which these worlds formed, affecting the delivery of volatiles, the terrestrial refractory budget, and potentially, Earth's overall habitability. To investigate the occurrence of Jupiter-like planets around inactive, low-mass (0.1-0.3M⊙) M dwarfs—which may host the only terrestrial planets amenable to atmospheric study with JWST—we monitored a volume-complete sample of 200 such stars over six years, collecting four high-resolution spectra per star. We did not detect any Jupiter-mass planets at Jupiter-like instellations, yielding a 95%-confidence upper limit of 1.7% on the occurrence rate of Jupiter analogs. In contrast, surveys of Sun-like stars have found that their giant planets are most common just beyond the snow line, at these Jupiter-like instellations. Our results indicate that solar-system-like architectures are rare around low-mass M dwarfs, with implications for the evolution and habitability of their terrestrial worlds.