Starting guard Nick Easton will also miss Sunday's game.
The news could not have come at a worse time for the Vikings, who are gearing up to face the division-leading Green Bay Packers Sunday.
Bradford missed three games before returning for last Monday's 20-17 win at Chicago but was ineffective and replaced in the final minute of the first half by backup Case Keenum.
The Vikings have gone 2-2 since Bradford's injury on the back of above average play from second-stringer Case Keenum. His timetable to return to the practice field is unclear.
Diggs, meanwhile, sustained a groin injury in the Chicago game and finished with just one catch for 4 yards. It is the second consecutive year Diggs has battled a groin injury. Keenum has played fairly well this season, with four touchdown passes and no interceptions.
Easton, who departed Monday's game with a calf injury, will likely be replaced by Jeremiah Sirles, who started 10 games for the Vikings a year ago, though most were at right tackle. It will be the first start this season for Sirles.
Bradford was joined by receiver Stefon Diggs, guard Nick Easton, safety Andrew Sendejo and defensive tackle Tom Johnson missed Thursday's practice.