Martinez appeared to jar his knee when challenging Vladimir Coufal in the second-half and initially continued before eventually being replaced by Raphael Varane.
United boss Erik ten Hag confirmed the injury looked “bad” after the game and reports from Argentine outlet TyC Sports claimed the former Ajax star is unlikely to return before the international break in March.
The 26-year-old is now confirmed to have sprained a collateral ligament in his knee, meaning surgery will not be required.
A club statement read: "Lisandro Martinez has sustained an injury to the medial collateral ligament in his knee and is expected to be out of action for at least eight weeks."
Martinez posted on social media: "I want to give a heartfelt thanks for the great support I've received and to reassure you that I'll soon be back out there, and we'll fight together. Always united!"