The officer responded to the call near 517 Leighton Ave. at 10:10 p.m. and was confronted by a man holding a weapon, Police Chief Kyle Westall said.
New Mexico State Police Lt. Tim Johnson said the man was Daniel Rey, 33.
Rey had thrown a small child from a bed, was striking a woman and was "breaking everything in the house," Farmington police Sgt. Joshua Laino said in a press release.
Rey had a "large edged weapon" and was shot. He was taken to San Juan Regional Medical Center where he died, Laino said.
Police didn't disclose any more specifics on the weapon Rey was carrying.
New Mexico State Police are investigating the shooting.
Johnson said the identity of the Farmington police officer who shot Rey won't be released until investigators have interviewed him. The agency did not release the officer's name Wednesday.
Johnson said a 17-year-old woman inside the home called police and said Rey had abused a 3 year old and the child's mother.
The officer who shot Rey was the first person to arrive on scene. The shooting took place inside the home before the second officer arrives, Johnson said.
The Farmington patrol officer has been placed on paid administrative leave while state police investigate the shooting, Laino said.
Witnesses in the neighborhood claimed hearing between three and six shots around 10:10 p.m.
Rey did not have any known criminal history in New Mexico or elsewhere, Johnson said.
Police investigators gathered evidence inside the home throughout the day Wednesday and crime-scene tape blocked off the home until Wednesday evening. Johnson said once investigators were finished with the scene they would let the family return to the home.
Tuesday's shooting was Farmington police's second officer-involved shooting this month.
On Jan. 1, Farmington police Sgt. Shawn Scott fatally shot Mark Chavez, a 49-year-old Farmington man.
Chavez had called police and told them a woman had been killed on Loma Linda Avenue, though police found no evidence of any dead person.
Chavez threatened Scott with a blunt object -- that police didn't identify -- and moved toward him when he was shot.
Scott remained on paid administrative leave Wednesday, Farmington police Lt. Taft Tracy said.
There are 119 officers within the Farmington police department and two are currently on paid administrative leave for fatally shooting suspects, Tracy said.
Prior to this month, Farmington police had not had an officer-involved shooting since December 2010.
When an officer is involved in a shooting they give initial statements needed for the investigation to other officers at the scene of the shooting and turn in their weapon and any other evidence, Tracy said.
They are given a day or two before they do an interview with investigators to "get their emotions in check," Tracy said.
During that interview, the law officer has the same rights as any other person being interviewed as part of a criminal investigation, which includes having an attorney present during questioning, Tracy said.
The officers have access to psychologists or other mental health care providers in the aftermath of the shooting.
If the officer is cleared of wrongdoing, the chief of police will evaluate the officer before clearing him to return to duty, Tracy said.
"Hopefully we have another extended period without" an officer-involved shooting," Tracy said. "But our officers will continue to do their job ... as they are trained."
Farmington Daily Times reporter Greg Yee contributed to this report.