The student who died at Northern Arizona University has been identified by the school as Colin Brough.
The victims being treated at Flagstaff Medical Centre are Nicholas Prato, Kyle Zientek and Nicholas Piring.
School public relations director Cindy Brown said the suspected shooter is in custody.
The shooting occurred in a car park outside Mountainview Hall dormitory at the north-east side of the Flagstaff campus.
Ms Brown said she did know what caused the shooting and did not have any details about the suspect or victims, their conditions and whether they were students.
The University tweeted that the situation had been stabilised and the campus was not on lockdown.
The four-year-old public University has more than 25,000 undergraduates.
Student Maria Gonzalez said that at first she suspected firecrackers.
“I was studying for an exam so I looked out the window and see two people running, and that’s when I realised they weren’t fireworks, they were actually gunshots,” she said.
“How am I supposed to feel safe where I’m learning?” she added.
Ms Brown said the wounded were taken to Flagstaff Medical Centre, which said it could not release any information on conditions.
The shooting came as President Barack Obama visited 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.
#NAUAlert: Details confirmed 4 victims, 1 fatality, 3 wounded. Shooter is in custody. Situation is stabilized. Campus not on lockdown.
— NAU (@NAU) October 9, 2015
THIS. NEEDS. TO. STOP. RT @AP: BREAKING: Official says 1 dead, 3 wounded in shooting at Northern Arizona University.
— rach 🟧 (@theresonlyus) October 9, 2015
Prayers to the families of Northern Arizona University
— Paige (@plstrudel) October 9, 2015
Another shooting. Another reminder that life is fragile at Northern Arizona University. Maranatha.
— Alen Andrews (@Alen_Andrews) October 9, 2015
Follow updates regarding the shooting at http://t.co/m91IA6yH5P: http://t.co/mdGo9DqG7w
— NAU (@NAU) October 9, 2015