According to authorities in the Mexican state of Veracruz, the accident occurred near the town of San Andres Tuxtla, about 500 kilometers away from Mexico City, on a road that ends up near the Mexican-Texan border.
The Mexican National Guard did not give immediate details of the condition of the injured or the causes of the accident.
However, Veracruz's civil protection agency said most of the injured migrants were taken to two nearby hospitals and a temporary shelter was set up to treat some of the more seriously injured.
Human rights defenders have long warned that Mexico's tougher stance on migration is likely to push migrants further into the shadows, forcing them to rely on smugglers and unsafe transportation means.
Reuters photos of the accident site showed a medium-sized white commercial truck overturned in a ditch, with the driver's window smashed.
The Mexican National Guard is currently working hard to prevent migrants from reaching the U.S. border after President Donald Trump threatened to impose fierce sanctions on countries that allow migrants to flow to U.S. borders.