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Hybrid light–matter coupled states, or polaritons, in magnetic materials have attracted significant attention due to their potential for enabling novel applications in spintronics and quantum information processing. However, most magnon‐polariton studies in the strong coupling regime to date have been carried out for ferromagnetic materials with magnon excitations at gigahertz frequencies. Here, strong resonant photon–magnon coupling at frequencies above 1 terahertz is investigated for the first time in a prototypical room‐temperature antiferromagnetic insulator, NiO,  inside a Fabry–Pérot cavity. The cavity is formed by the crystal itself with a thickness adjusted to an optimal value. Terahertz time‐domain spectroscopy measurements in magnetic fields up to 25 T reveal the evolution of the magnon frequency through Fabry–Pérot cavity modes with photon–magnon anticrossing behavior, demonstrating clear vacuum Rabi splittings exceeding the polariton linewidths. These results show that NiO is a promising platform for exploring antiferromagnetic spintronics and cavity magnonics in the terahertz frequency range.