"Thirteen dead is the official figure, all of them by landslides caused by rains from Fernand," a spokesman for the civil protection agency told AFP.
The victims were from three municipalities in central Veracruz, where Fernand came ashore early today from the Gulf of Mexico.
Heavy rains and high winds led to flooding and damage to more than 100 houses, forcing some 300 people to flee to higher ground, officials said.
The US National Hurricane Center said the storm was expected to dump four to eight inches of rain on Veracruz.
Fernand is the fifth named storm this year in the Atlantic, where the hurricane season runs from June 1 to November 30.
The US National Oceanic and Atmospheric Administration has forecast a more than usually violent season of 13 to 19 named storms including six to nine hurricanes.