Police arrested the suspected gunman, who was also a member of the Guard, at about 1810 GMT, and the wounded members of the Army National Guard did not suffer life-threatening injuries, said Patrick Foughty, spokesman for Naval Installations Command in Washington.
The shooting in Millington, Tennessee occurred across the street from a naval base on land leased by the Army National Guard, he said.
"There was a shooting. The shooter is in custody," Foughty told AFP.
The Millington naval base handles personnel administration for the Navy, officials said.
The American military is reviewing security at all its installations after a deadly shooting spree on October 16 at the US Navy Yard in Washington in which a former sailor working as a contractor opened fire inside an office building.