Fourteen people were injured, six of them critically, the Minneapolis Star Tribune reported.
Mohammed Cheikhadobi, an advocate for the Somali community, said at a news conference three residents of the building, which is next to a mosque that also was damaged in the fire, had not been accounted for, KARE-TV, Minneapolis, reported.
"My concern is for the victims, to their families and that they get adequate support," Minneapolis City Councilman Abdi Warsame said. "I mean obviously their homes are destroyed, and so shelter, food, medical support. That's my main concern right now."
The fire was reported at about 8:15 a.m. But hours later, no one had been able to enter what was left of the building to search for victims or to try to find the cause of the fire.
Minneapolis Fire Chief John Fruetel said low temperatures made the firefighting effort difficult.
"These are very treacherous conditions," he said.
Ahmed Muse, one of the owners of the Otonga Grocery Store, said he experienced what he called "an electrical shock" shortly after he arrived at 8 a.m. He said that was followed by an explosion on the second floor that blew out windows.