The accident happened when the trains started moving, the mayor of the city, Claudia Sheinbaumsaid on Twitter.
The person killed was a young woman, while the 22 injured do not appear to be in serious condition, chief of city security Omar Garcia told local media Grupo Milenio.
Four others trapped on a carriage on Line 3 were rescued and are in good health, he added.
There have been several accidents in the subway in recent years. The most serious was the collapse of a railway viaduct on line 12 in May 2021, which killed 26 people and injured more than 60.
Deficiencies in maintenance were identified as one of the causes of that accident.