"We have several victims, about 13, they are in various medical facilities", Lajous told the channel FOROtv.
The incident reportedly happened on Sunday morning.
One eyewitness told FOROtv that the group of pilgrims included about 20 runners and four cyclists. According to the source, the police blocked the car that had hit the victims, so that the driver could not flee from the scene.
The driver and a passenger in the car have both been arrested, the channel reported.
According to the media, the Attorney General's Office of Mexico City has launched an investigation into the accident.