"Details confirmed 4 victims, 1 fatality, 3 wounded. Shooter is in custody. Situation is stabilised. Campus not on lockdown," university officials said on Twitter.
NAU is located in the city of Flagstaff in Arizona.
The motive for the shooting was not clear and Northern Arizona officials have not said if the dead victim was a student.
In an earlier Twitter message, university officials urged residents of the Mountain View Hall dormitory to stay indoors.
The deadly Arizona shooting follows the high-profile October 1 shooting rampage at Umpqua Community College in Oregon, in which a 26 year-old gunman shot dead nine people, then committed suicide.
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