The 30-year-old will not be given a timeframe for his recovery until surgery has been completed on Thursday.
Vunipola, who has won 67 England caps, has not played international rugby since the defeat by South Africa in November.
He suffered the injury while carrying the ball in the first half of the quarter-final showdown at Stade Marcel-Deflandre on Sunday and had to be carried from the pitch on a stretcher.
"Billy suffered a knee injury during Sunday's Champions Cup quarter-final against La Rochelle. He will therefore miss the remainder of the 2022/23 season. We're all behind you, Billy!" a Saracens statement read.
Vunipola's form, combined with the failure of Alex Dombrandt to convince in the No.8 jersey, raised the prospect of an England comeback with the World Cup in France starting in September.
But Vunipola, who is rumoured not to be on speaking terms with England boss Steve Borthwick, has now been denied the opportunity to press his claim on the pitch.
