The injured are in a stable condition in hospital, but Providence Mayor Brett Smiley warns the number of casualties could rise
The suspect remains at large - police say the attacker was a male dressed all in black who fled on foot
One person was arrested before police determined they had no involvement in the shooting and released them
A shelter in place warning is still in effect for the greater Brown University area
President Donald Trump says he has been briefed on the shooting, which happened at 16:05 local time (21:05 GMT) on Saturday
Steph Machado, a reporter for the Boston Globe, has been telling BBC News about the atmosphere around Brown University.
Restaurants around the campus have locked their doors, she says, with staff and customers waiting inside until the emergency order is lifted.
"There are flashing lights everywhere," she adds.
The campus is usually a place "where people feel very safe walking around", Machado says. The typically busy student area is "eerily quiet" tonight.
Nearly four hours after the shooting, Brown University continues to tell its students to keep their doors locked and avoid moving across campus.
The eastern edge of the Providence campus is under lockdown, as the manhunt for the suspected shooter in surrounding neighbourhoods is ongoing.
"We know this is a source of tremendous fear and anxiety across our community right now," the university's president, Christina H Paxson, says.
"We continue to be in lockdown, and it is imperative that all members of our community remain sheltered in place."
