Wasps say a full recovery is expected to take around eight weeks, which would sideline him until mid-June.
Vickery, who led England at last autumn's World Cup and in the RBS 6 Nations Championship this season, suffered a tear to the medial collateral ligament of his right knee.
He underwent a scan earlier on Wednesday, which revealed the extent of his injury.
Wasps have four Premiership games remaining against Saracens, Gloucester, Newcastle and Leeds Carnegie.
Having won their last seven league matches, they are well on course to secure a play-off place in the title race.
Wasps rugby director Ian McGeechan said: "Losing a player of Phil's calibre and experience is obviously a major blow, especially at this crucial time of the season.
"However, the busy schedule we've been faced with recently has demonstrated the strength that we have throughout the Wasps squad.
"With careful management, allied to the spirit and determination the players are showing, we are confident we can remain competitive for the remainder of the season."