Photo: Hurricane Beatriz
The Pacific ports of Acapulco, Manzanillo and Zihuatanejo are closed.
The US National Hurricane Center said winds rose to 150km/h (90mph), with the storm moving over the coast.
Tourists have been sheltering in their hotels, with reports of one tourist injured by a falling tree in Acapulco.
Early on Tuesday, Beatriz was located about 20km (15 miles) south-east of La Fortuna and 80km (50 miles) west-northwest of Manzanillo, moving northwest at about 20 km/h (13mph).
It was expected to drop 15-30cm (6-12in) of rain along the coast, with a risk of flash floods and mudslides.
The category 1 hurricane is expected to weaken and move away from the coast by the end of Tuesday.