Soldiers were shooting at the tires, but at least one bullet struck and killed the youth, according to the statement.
A 19-year-old passenger was taken into custody.
Human rights groups have alleged abuses by soldiers deployed for more than a year as part of President Felipe Calderon's nationwide anti-drug offensive.
In June, 19 Mexican soldiers were charged with homicide in the killings of two women and three children whose vehicle failed to stop at a checkpoint in the Pacific Coast state of Sinaloa.
More than 24,000 agents have been sent to several states plagued by drug violence, including Calderon's home state of Michoacan in western Mexico.
