They were found near the village of Tultepec while drains were being installed.
The bones are believed to be about 14,000 years old and were scattered, suggesting the mammoth had been cut up by humans for its meat and pelt.
Other remains have been found in the area which had been a shallow lake where the heavy mammoths got stuck.
Luis Cordoba, an archaeologist with the National Institute of Anthropology and History told French news agency AFP that the remains of more than 50 mammoths had been discovered in the area around the capital, Mexico City.
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Human relics
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He said the Tultepec mammoth had been found 2m beneath a street in the village.
He said when alive it had been between the ages of 20 and 25, and the skeleton was almost complete and well-preserved with tusks still attached to its skull.
Scientists hope to eventually assemble the fossils and put them on display.
Mammoth remains have been discovered in several regions of Mexico, in areas near lakes where herds congregated.
Known as the Columbian Mammoth, they were a sub-species which lived across the United States and Central America.
Remains of the mammoths have been uncovered across Mexico, Texas and as far west as the La Brea Tar Pits in California.
Mexican experts say they are completing work on digging up fossilised bones of a mammoth found near Mexico City.