In the village of La Pintada, near the Pacific coast, a landslide partially engulfed the town.
At least 15 bodies have been recovered and almost 70 residents are missing, the authorities said.
Tropical Storm Manuel, which on Thursday briefly became a hurricane, has now moved north, forcing hundreds from their homes in Sinaloa state.
As it hit the land, Manuel brought torrential rain and winds of up to 120km/h (75mph) and caused flash floods in Sinaloa.
Schools in the region have been closed and a fishing village of Yameto was evacuated as Manuel approached.
More than 100,000 were affected by the hurricane, the State governor, Mario Lopez Valdez told reporters.
It then gradually began losing strength, according to the United States National Hurricane Center, going back to being a tropical storm.
Manuel is now expected to dissipate before the weekend.
However, weather conditions are expected to remain poor over the coming days as a third storm is forecast.
With the Gulf Coast having been hit by Hurricane Ingrid, this week was the first time since the 1950s that Mexico has had to deal with two storms simultaneously, the BBC's Will Grant in Mexico City says.
The resort town of Acapulco and its surrounding areas were worst hit by Manuel earlier in the week.
Since then, more than 10,000 stranded tourists have been airlifted by military planes out of the resort town of Acapulco.
Several stores have been looted and residents of the outskirts of Acapulco have complained about being left to fend for themselves.
Residents of La Pintada, a remote village of about 600 people north-west of Acapulco, described how the hillside buried their homes as they were holding independence day celebrations on Monday evening.
The landslide tore through the middle of the village, destroying the church, the school and the kindergarten.