The massive explosion by the January 14, 2022 Hunga Tonga-Hunga Ha’apai volcano in Tonga triggered a trans-oceanic tsunami generated by coupled ocean and atmospheric shock waves during the explosion. The tsunami reached first the coast of Tonga, and later many coasts around the world. The shock wave went around the globe, causing sea perturbations as far as the Caribbean and the Mediterranean seas. We present the effects of the January 14, 2022 Tonga tsunami on the Mexican Pacific Coast, Gulf of Mexico, and Mexican Caribbean coast, and discuss the underrated hazard caused by great volcanic explosions, and the role of early tsunami warning systems, in particular in Mexico. The shock wave took about 7.5 hours to reach the coast of Mexico, located about 9000 km away from the volcano, and the signal lasted several hours, about 133 hours (5.13 days). The first tsunami waves recorded on the Mexican Pacific coast arrived around 06:26 on January 15, at the Huatulco, Oaxaca tide gauge station. The maximum tsunami height exceeded 2 m at the Ensenada, Baja California, and Manzanillo, Colima, tide gauge stations. Most tsunami warning advisories, with two exceptions, reached communities via social media (Twitter and Facebook), but did not clearly state that people must stay away from the shore. We suggest that, although no casualties were reported in Mexico, tsunami warning advisories of far-field tsunamis and those triggered by volcanic eruptions should be improved and reach coastal communities timely, explaining the associated hazards on the coast.