Videos on social media from different parts of the affected areas showed streets turned into rivers carrying away vehicles and houses almost completely covered in water, AP reported.
Mexico deployed 8,700 military personnel to assist the population.
One of the hardest hit areas was the central state of Hidalgo, where 16 deaths have been reported, according to state Interior Secretary Guillermo Olivares Reyna.
At least 1,000 homes, 59 hospitals and clinics, and 308 schools have suffered damage in the state because of landslides and rivers topping their banks. Some 17 of the states 84 municipalities were without electricity, he said.
In neighboring Puebla State, nine people died and 13 were missing, according to Gov. Alejandro Armenta. He requested help from the federal government to rescue 15 people, including some children, who were stranded on rooftops by floodwaters. He estimated some 80,000 people were affected by the heavy rains and said a gas pipeline was ruptured by a landslide.
In the Gulf coast state of Veracruz, two people died, including a police officer, Gov. Rocio Nahle said. Some 5,000 homes were damaged and the Navy evacuated nearly 900 people to shelters. The city of Poza Rica was one of the hardest hit by river flooding. Authorities cut electricity as a precaution.
Earlier, authorities in the central state of Queretaro confirmed that the child had died after being caught in a landslide.
The heavy rainfall also caused power outages affecting more than 320,000 users and damage to almost 1,000 kilometers of roads in six states, authorities said.