Tropical Storm Fernand is expected to weaken to a tropical depression later in the day as it moves across Mexico.
The storm's maximum sustained winds early Monday are near 45 mph (75 kph).
A tropical storm warning is in effect on Mexico's coast from Veracruz north to Barra de Nautla.
The government of Veracruz state has advised its 7.7 million residents to stay home, and Gov. Javier Duarte suspended classes in the whole state to protect children from venturing out into winds and rain.
Fernand is centered about 60 miles (100 kilometers) northwest of Veracruz and is moving west-northwest near 9 mph (15 kph).
The storm is expected to bring 4 to 8 inches of rain over parts of several states as it moved toward central Mexico.