Ten more migrants were reportedly hurt in the incident on Tuesday night, which happened about 25 miles (40 km) north of the Guatemalan border, according to the Mexican Defense Ministry.
According to the ministry, a military patrol observed the migrants’ pick-up truck driving quickly and appearing to try to elude detection.
According to the statement, soldiers reported hearing explosions, and two officers then opened fire. They said that the officers had been removed from their positions until an inquiry is conducted.
The US is putting pressure on Mexico to reduce the number of migrants passing through it.
The troops pursued the car after it failed to halt at an army checkpoint and then fired bullets in an attempt to stop it, according to a police report into the incident in the southern state of Chiapas, the Reuters news agency said.
It said that the driver attempted to flee by turning off onto a gravel road, but he lost control of the car.
In a statement, the defense ministry said that the migrants were from Pakistan, India, Egypt, Nepal, and Cuba. The nationalities of the deceased were not provided.