Max became a Category 1 hurricane on Thursday, the U.S. National Hurricane Center (NHC) said, moving toward Mexico's tourist-laden Pacific coast and bearing down on a region that includes resorts like Acapulco, Zihuatanejo and Ixtapa.
Max was blowing maximum sustained winds of 120 kilometres per hour on Thursday morning, the NHC said, and was about 88 km southwest of Acapulco.
The storm is moving east at 10 km/h, the NHC added.
"An east or east-northeast motion is expected to continue until Max moves inland along the southwestern coast of Mexico later today," the NHC said.
Max could strengthen before reaching the coast but would likely weaken once it hit land, the NHC said. In the state of Guerrero, home to some of Mexico's major tourist resorts, Max could dump as much as 25 cm of rain, the NHC said.
The storm is bad news for Acapulco, which is already struggling with endemic gang violence. Although it is not peak season, many tourists were likely to travel there to celebrate Mexico's Independence Day celebrations at the weekend.
Max arrives a week after a powerful 8.1 magnitude quake shook southern Mexico, destroying buildings in the state of Oaxaca and killing at least 98 people nationwide.
Max is the seventh official hurricane of the Pacific season, although damages have been limited in comparison with the ravages of Atlantic hurricanes Harvey and Irma.