Deputy Security Minister Ricardo Mejia said four arrest warrants had recently been issued against military officials over the notorious abduction of the 43 students in the southwestern city of Iguala in 2014.
"At the moment, three of them have been carried out and there are three detainees, including the commander of the 27th infantry battalion at the time," Mejia told a news conference.
Rodriguez was in charge of the unit during the abductions, which the previous government said were done by corrupt local police working in cahoots with a local drug gang.
After presenting a review of the case by the current administration, Deputy Interior Minister Alejandro Encinas said in late August six of the missing students were handed over alive to Rodriguez and that he had ordered them killed.
Asked for comment about the accusations against Rodriguez, Mexico's Defense Ministry said it had no information.
The government referred to the case as a "state crime" in its report, which alleged local, state and federal authorities, including the Army, were complicit and involved in a cover-up of the students' disappearances.
The Army was at the time commanded by Salvador Cienfuegos, who was later at the center of a diplomatic spat with the United States when he was arrested by U.S. officials at Los Angeles airport on drugs charges in 2020.
He denied any wrongdoing and the case was subsequently dropped.
Two Mexican officials said the government did not have plans to go after Cienfuegos over the disappearances.
News of Rodriguez's arrest comes a day after the lower house of Congress voted to keep soldiers on the streets to oversee public security until 2028, feeding concern about the amount of power President Andres Manuel Lopez has given the Army.