Five others were injured by the blaze in a rural area close to Mexicali, near the border with the US.
Some 45 elderly people lived at the nursing home, a non-governmental organisation employee told local media.
She said the facility, called "Beautiful Dawn", housed formerly homeless people.
The mayor of Mexicali, Jaime Diaz Ochoa, said 23 residents had been taken to a temporary city shelter.
He said the authorities were trying to determine the cause of the deadly blaze.
A fire that broke out early on Tuesday at a home for the elderly in north-western Mexico has killed at least 15 people.