The Minneapolis Police Department said two of its officers were among those wounded in the incident on Wednesday, and warned the public to stay away from the area.
Police did not immediately say how many people were shot, but Hennepin County Medical Center said it received seven patients, including one who died.
No additional information was immediately released about the conditions of the other patients.
Video posted to social media showed police aiming rifles upward at an apartment tower near the Minneapolis Convention Center.
Officials warned residents to avoid the densely populated Loring Park neighbourhood nearby.
Minnesota Governor Tim Walz said on social media that state officials are on the ground helping local law enforcement respond to the shooting.
"Grateful to law enforcement actively working to ensure the safety of our neighbours in Downtown Minneapolis this afternoon," he wrote.
"Minnesota is praying for our first responders."
"The FBI is responding to the shooting and "will offer any and all resources necessary to assist local authorities," director Kash Patel said on X.
Minnesota House Speaker Lisa Demuth said she is praying for the victims of "this heinous crime".
"I'm incredibly thankful for the massive response of our brave law enforcement officers," she said on social media.
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