The shooting unfolded shortly after 11am in a residential area in the town of Farmington, about 180 miles north of state capital Albuquerque.
Two police officers were wounded in an exchange of gunfire with the suspect, who was killed at the scene.
Both were reported to be in a stable condition at a local hospital.
There were multiple civilian victims, at least three of whom died, the Farmington Police Department said.
The shooter is believed to have acted alone, according to police.
Several public schools in Farmington were locked down during the shooting, but police said after the suspect was killed that there was no longer a threat to the public.
The shooting marks the 34th mass shooting of May 2023 amid increasing calls for states to tighten gun control laws.
There have been more than 215 mass shootings in the US so far this year, according to the Gun Violence Archive (GVA).
The GVA defines a mass shooting as one in which four or more people were either injured or killed.
Separately, two people were killed and five others injured in a shooting in southwestern Arizona on Saturday night. Victims ranged from 15 to 20 years old.