Part of a hillside collapsed in the municipality of Jilotzingo near the capital, according to the civil protection service in the State of Mexico.
"A landslide swept away eight houses, leaving 12 people under the rubble and, unfortunately, the loss of a three-month-old child," it said on social media platform X.
Emergency services assisted by rescue dogs freed three people who were taken to hospital, it said, adding that the search for other survivors continued.
Television images showed rescuers digging in the mud with shovels.
Residents, some holding small children, were seen leaving the area with whatever belongings they could carry.
One man told Foro TV that water had been pouring downhill "like a waterfall" at the time.
Another said she had heard "a rumble, like something was breaking," adding that there was heavy rain and lightning at the time.
"I'm very scared," she added.
Landslides are common in Mexico, which is regularly hit by natural disasters such as earthquakes and hurricanes.
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