The 35-year-old landed awkwardly in the closing stages of normal time at Old Trafford and required treatment on the field before limping off and being replaced as the match went into extra time.
Initial reports suggested that Ibrahimovic would miss the remainder of the season with the injury, but ESPN claims that the problem is even more serious than that.
The Swede could now be sidelined until January after a scan reportedly showed ligament damage to his knee, putting his future at the club in further doubt.
Ibrahimovic's current deal at Old Trafford expires at the end of this season and, while the club have been keen to tie him down to at least another year, the player is yet to make a decision on his next move.
Ibrahimovic is United's top-scorer this season with 28 goals in all competitions, but hopes of a bumper contract either at Old Trafford or abroad could be affected if he is unavailable until 2018.