Two other people were injured and were being treated at a hospital, Robinson said.
The shooter, who carried one weapon, died of a self-inflicted gunshot wound, authorities said.
On Tuesday afternoon, the shooter opened fire after going to the neurology office of Nevada Advanced Medicine on the third floor, said Sharon Spangler, spokeswoman for Reno Police.
Earlier, the University of Nevada police tweeted that there was an active shooter and faculty, staff and students should find shelter where they were.
CNN first learned of the shooting through the university police department’s Twitter account.
The medical center describes itself as the only Level II trauma center in that region of Nevada and is home to the area’s only Children’s Hospital, its website says. The facility also offer the region’s largest number of clinical research trials.
Last month, there was a hospital shooting in Wisconsin when police shot and wounded an armed man at a Milwaukee-area children’s hospital’s neonatal intensive care floor, authorities said.
Milwaukee police had gone to the Children’s Hospital of Wisconsin to arrest the man on a felony warrant and found him holding a child in the intensive care unit, authorities said. Instead of surrendering, the man took out a handgun and fled down a hallway, prompting police to shoot him.