The state worst hit is Puebla, where officials say 28 people died. Another 10 people were killed in the state of Veracruz.
Previously, the confirmed number of deaths was six.
Earl made landfall in Belize this week as a Category One hurricane, after causing destruction in the Caribbean.
The storm was later downgraded to a tropical depression but it still left a path of destruction in Mexico.
Most of the victims were in the remote town of Huauchinango, Puebla.
They died after their houses were engulfed by tonnes of mud and rocks.
A whole hill collapsed near Huauchinango, sweeping down on a nearby village, officials say.
"It is a tragedy what has happened to our people in Huauchinango," Mayor Gabriel Alvarado was quoted as saying by the Associated Press.
Heavy rain continued in the region, forcing officials to close a section of the main federal motorway to the capital Mexico City.
Earlier this week, at least nine people died due to extreme weather in Haiti and the Dominican Republic as the storm passed over the Caribbean.
The death toll in Mexico's landslides and flooding has jumped to 38 after Tropical Storm Earl swept through the country's eastern regions.