The gunfire erupted in a parking lot at the Northern Arizona University, school public relations director Cindy Brown said.
The lot is just outside Mountainview Hall dormitory at the northeast side of the Flagstaff campus, she added.
Student Maria Gonzalez told The Associated Press that she at first suspected firecrackers.
“I was studying for an exam so I looked out the window and see two people running, and that’s when I realized they weren’t fireworks they were actually gunshots,” she said.
The first police call about the gunfire came in at 1:20 a.m. PDT.
Brown said she didn’t know what caused the shooting and also didn’t have any details about the suspect and victims, their conditions and whether they are students.
On its website, the university said that the campus was stabilized and the campus was not on lockdown.
“How am I supposed to feel safe where I’m learning,” Gonzalez said.
Brown said the wounded were taken to Flagstaff Medical Center, which said it couldn’t release any information on conditions.
Both university and Flagstaff police are investigating.
The Flagstaff shooting comes on the same day that President Obama is scheduled to visit Roseburg, Oregon, where eight students and a teacher were shot and killed last week at Umpqua Community College. The gunman in the Oregon shooting wounded nine others before turning the gun on himself.
NAU plays a major role in the northern Arizona city of Flagstaff.
The 4-year public university has more than 25,000 total undergraduates.