Cook is expected to miss at least the next two games -- Sunday at the Detroit Lions and the following Thursday against the Pittsburgh Steelers -- with the hope being he can return the next week for the Monday, Dec. 20, game at the Chicago Bears, the source told Schefter.
Vikings coach Mike Zimmer would not disclose the nature of Cook's injury Monday and said his star running back was "day-to-day."
"That's what they're telling me," Zimmer said.
Cook was carted off the field late in the third quarter and ruled out for the remainder of the game.
He was injured after being brought down by Niners defensive tackle Kevin Givens following a handoff. The running back lost the ball in the process of being tackled and immediately grabbed for his chest with his right arm when he hit the ground.
He remained down on the field for several minutes as athletic trainers tended to him. Both Vikings and Niners players knelt around Cook while he was moved onto a cart before being taken off the field and back into the locker room for further evaluation.
Cook's day ended with 10 carries for 39 yards and six receptions for 64 yards. He was replaced by backup running back Alexander Mattison, who rushed three times for 8 yards and caught one pass for 2 yards after Cook left.
In other news Monday, the Viking placed cornerback Patrick Peterson on the reserve/COVID-19 list, putting his availability for Sunday's game against the Lions in question.
ESPN's Courtney Cronin contributed to this report.