Glasgow's back row resources are already stretched with Jack Dempsey, Matt Fagerson, Gregor Brown and Sintu Manjezi unavailable through injury.
Vailanu received treatment after a no-arms tackle from Hamish Watson in the 15th minute of last Friday's 1872 Cup first-leg encounter. Vailanu played on with heavy strapping on his leg.
"It's more serious than we thought," said Warriors head coach Franco Smith on The Offside Line. "The no-arms tackle in rugby is sometimes more dangerous than the head collisions. We've got him and Gregor Brown both sidelined with similar injuries now. For Sione we're looking at six to eight weeks out, it sounds like at this stage."
Glasgow Warriors players who are currently unavailable for selection: Fraser Brown (knee), Gregor Brown (knee), Sebastian Cancelliere (neck), Jack Dempsey (face), Jamie Dobie (ankle), Matt Fagerson (face), Sintu Manjezi (foot), Enrique Pieretto (knee), JP du Preez (knee), Ollie Smith (knee), Lucio Sordoni (shoulder), Kyle Steyn (ankle), Sione Vailanu (knee), Murphy Walker (knee).