The first disaster happened Saturday in the village of San Luis Ayucan, near the capital, the national civil protection agency said.
Nine bodies were recovered and rescue teams using sniffer dogs were able to save three people from the mounds of mud left by the landslide.
An infant was confirmed dead that same day, but it was not clear if this death was part of the nine.
Nearly 150 people in the village were forced from their homes and are now living in shelters.
Then on Monday heavy rain caused another landslide that buried a house in the nearby municipality of Naucalpan, the national civil protection agency said on X.
Local authorities confirmed to the channel Televisa that six people, apparently members of the same family, died trapped in the home, while three others were injured.
Landslides are common in Mexico, especially in the rainy and hurricane season running from May to November.