The suspected gunman was identified as Steven Jones, a freshman at the university, campus police chief Gregory Fowler said. He said Jones pulled the handgun in a "confrontation" with several students.
Colin Brough was killed in the shooting, according to the university. The three injured students, identified as Nicholas Prato, Kyle Zientek and Nicholas Piring, suffered multiple gunshot wounds and were being treated at Flagstaff Medical Center, Fowler said. Their conditions were not disclosed.
The shooting occurred just hours before President Barack Obama was scheduled to visit Roseburg, Oregon to meet privately with families of nine people killed in a mass shooting at a community college there last week.
A university spokesman said the Arizona incident occurred in a parking lot next to a residence hall for Greek organizations - fraternities and sororities. The shots were reported at 1:20 a.m., officials said.
"We don't know the facts yet about what brought them together, or what caused the confrontation," Fowler said.
Profiles for people named Colin Brough, Nicholas Piring and Kyle Zientek on Linkedin list them as business students at the university with links to the Delta Chi fraternity, although school officials did not immediately confirm those ties.
A spokeswoman for the university initially identified the shooter as a member of the Delta Chi fraternity but later retracted the statement.
Delta Chi confirmed in a statement to local broadcaster KPNX-TV that frat members were involved in the shooting, but said the incident "had no ties to the chapter."
Jones, who did not try to run, was arrested by university police and is cooperating with authorities, Fowler said.
Guns are not allowed to be carried on Northern Arizona University's campus under Arizona law and Arizona Board of Regents policy, Fowler said.
The campus was secure and classes were to go on as scheduled on Friday, university president Rita Cheng told a news conference. Cheng called the incident "isolated."
"Our hearts are heavy," Cheng said.
About 20,000 students attend classes at the Flagstaff campus, according to the school's website.
"I join Arizonans from all across our state in praying for the victims of this morning's tragic shooting, their families and the entire Northern Arizona University community," said Arizona Governor Doug Ducey, a Republican.
Obama reacted to the Oregon killings by vowing to step up efforts to curb gun violence in the United States. Gun rights advocates said the Oregon shootings underscored the importance of the right of Americans to bear arms and defend themselves.