Masi has had surgery after suffering the setback in his side's Aviva Premiership defeat at Sale Sharks late last month.
The 32-year-old damaged his posterior cruciate ligament and medial collateral ligament and will have to undertake a lengthy rehabilitation regime before hopefully returning to action in late January or February.
That means Masi will miss all six group games as Wasps look to add a second Amlin Challenge Cup crown to their 2003 success.
Wasps have been drawn against Bayonne, Grenoble and Viadana in Pool 4 and Masi will hope his side can finish top of the pile to give him a chance of featuring when the knockout stages begin in early April.
"London Wasps back Andrea Masi this week underwent surgery on the knee injury he suffered in the game against Sale Sharks," read a statement on the Wasps website.
"Masi suffered damage to both his MCL and PCL and will be on the sidelines for a period that is estimated to be between 16 and 20 weeks."
Wasps kick off their campaign against Viadana in Italy at the Stadio Comuncale Pierluigi Zaffanella a week on Saturday. They then host Bayonne at Adams Park the following Thursday, before a December double header with Grenoble.