Fernand has weakened to a tropical depression, but it is still bringing heavy rains to eastern Mexico.
The system's maximum sustained winds Monday decreased to near 35 mph (55 kph), several hours after making landfall.
The government of Veracruz state has advised its 7.7 million residents to stay home, and Gov. Javier Duarte suspended classes in the state to protect children from venturing out into winds and rain.
Fernand is centered about 50 miles (85 kilometers) south-southwest of Tuxpan and is moving 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.