Authorities said the shooter had died but did not specify whether that person was among the three reported dead.
Aztec police chief Mike Heal told reporters that the suspect was down, without clarifying if "down" meant injured, dead or in police custody.
Authorities haven't identified the shooter or the victims.
Other schools in the area were also locked down. Christesen did not say if the dead included the shooter.
Deputies with the sheriff's office and surrounding police departments responded to the school after reports of a shooting. Parents are able to pick up their children at 516 and Mesa Verde, after they are checked in and accounted for.
Aztec High School is about 180 miles northwest of Albuquerque, New Mexico.
Sheriff Ken Christesen confirms the shooting at Aztec High School on Thursday morning.
Per the statement, the school will be placed on lockdown for roughly "three to four hours".