Police cordoned off an area of the city center full of bars and nightclubs. Witnesses said they were busy on Saturday night with many people eating and drinking outside.
Cara Curran, an organizer of the club, said she saw several people fighting in the streets.
“It was a group of boys against another group of boys,” she told the BBC, adding that “racist slurs” were being launched.
Foreign Minister Dominic Raab said it was “a very serious incident. Our thoughts and prayers are with the victims and their families ”.
He said he had no information to suggest the stabbings were linked to terrorism.
Emergency services were on the scene to ensure the injured received medical attention. Police said the response would continue “for a while” and urged people to stay away from the area.
West Midlands Mayor Andy Street urged people “not to speculate on the incident” and to “remain calm but vigilant”.