The Chile international received treatment during the 2-1 quarter-final win over Bayer Leverkusen in Dusseldorf on Tuesday (AEST) and finished the match with heavy strapping over his right thigh.
In a statement released on Wednesday, Inter confirmed: "Alexis Sanchez underwent medical tests this morning in Duisburg after suffering an injury during our match against Bayer Leverkusen.
"The tests confirmed that he has suffered a strain in his right hamstring. His condition will continue to be reassessed over the next few days."
Inter faces Shakhtar Donetsk, which beat Basel 4-1 in the last eight, in a semi-final clash in Dusseldorf on 18 August (AEST).
Sanchez, 31, has made 30 appearances for Inter in 2019-20.
After initially joining on loan from Manchester United, he made the move permanent last week after the Red Devils reached an agreement over rescinding his contract.