England winger Elliot Daly will see a specialist on Wednesday to find out if he requires surgery on the ankle injury.
Number eight Nathan Hughes and fly-half Jimmy Gopperth will also see a specialist on Wednesday to assess knee injuries.
In a statement on the club’s website, Wasps director of rugby Dai Young said: “Our club doctor has taken a look at Nathan Hughes, Elliot Daly and Jimmy Gopperth to assess the injuries they suffered against La Rochelle.
“He thought they should all get an MRI scan, and when the scans came back it didn’t look particularly good news.
“They are all seeing specialists tomorrow (Wednesday), so we’ll know more then, but we can certainly say they’ll be out for a few weeks.
“Elliot has injured his ankle. He has a syndesmosis injury, which is pretty common.
“He is going to see the specialist to see whether any surgical intervention is required, which depending on the grade of the injury hopefully it won’t be.
“Jimmy and Nathan both have MCL injuries to their knees. Again, we’re waiting on the specialist to let us know what is required, but we can safely say even the best picture, which is a grade one tear, will require a minimum of four weeks.”