Coach Mike Zimmer officially declared him out after Friday's practice.
Bradford didn't practice Friday and reportedly departed town to receive a second opinion from Dr. James Andrews. Zimmer declined to confirm or deny the visit to Andrews.
Case Keenum will make his second consecutive start for the Vikings.
Bradford twice tore the ACL in the left knee (2013, 2014) but said he doesn't feel the current injury is related to those situations.
"This particular issue we're dealing with, I'm not sure if I've ever dealt with it before," Bradford said earlier this week.
Asked about the possible length to Bradford's absence, Zimmer replied, "I don't have a crystal ball. All I know about is this week."
Bradford suffered the injury in Week 1 when he passed for 346 yards and three touchdowns against the New Orleans Saints. He said it a noncontact injury and that he experienced pain and swelling after the game.
Bradford was a limited practice participant on Wednesday and Thursday before missing Friday's workout.
Keenum was 20-of-37 passing for 167 yards in last Sunday's 26-9 loss to the Pittsburgh Steelers.