The official said the wounded were not agents of the Drug Enforcement Administration or FBI.
The U.S. Embassy had no immediate comment.
A Mexican army official said the SUV with diplomatic plates was found after a report about a shootout on the two-lane highway. The army official was not authorized to be quoted by name. He said a Mexican navy captain was also in the vehicle, but was not injured.
The Toyota vehicle was riddled with bullets, most concentrated around the passenger-side window, indicating possible involvement by experienced gunmen.
The shooting occurred on road winding through a mountainous area where drug gangs, common criminals and leftist rebels have been known to be active in the past.
Attacks on diplomatic personnel were once considered rare, but this is the third attack in two years.
In 2011, one U.S. Immigration and Customs Enforcement agent was killed and one wounded in a drug gang shooting in northern Mexico.
A drug-gang shooting In 2010 in the border city of Ciudad Juarez killed a U.S. consulate employee, her husband and another man.