Photos from the scene on Oct. 22 showed a white sheet covering the body, with police vehicles nearby and cones and police tape keeping people away from the dead man.
The body was later taken to the Forensic Medical Service in the center of Tapachula.
“It’s dangerous, there are no ambulances and if the children faint, they can die because there is no help,” he told the broadcaster. “Today we saw that a man died when he fell from a truck.”
No other deaths have been reported.
The caravan was traveling north to try to reach the United States-Mexico border, where migrants hope to cross into America.
President Donald Trump and other U.S. officials have said they won’t allow that to happen, with Trump saying he'd send the military to the border if Mexico was unable to stop the migrants.
He also said that migrants who didn’t apply for asylum in Mexico would not be eligible to apply for asylum in the United States.