Pogba will miss the visit of West Ham and also looks doubtful for the upcoming Europa League last-32 double-header against Real Sociedad, as well as top-flight meetings with West Brom, Newcastle and Chelsea.
“He’s just started his recovery, working with the medical staff and we’ll get him back as soon and as safely as we can.
“Of course, Paul has been very important for us and we’re not going to take any risks. [So it is] a few weeks definitely. “
Manchester United centre-back Eric Bailly is now back in training after injury, but Solskjaer expects him to miss the FA Cup tie against West Ham.
Phil Jones is the Red Devils’ only other confirmed absentee as he continues his recovery from summer knee surgery.
Man Utd predicted lineup: Henderson, Wan-Bissaka, Lindelof, Maguire, Shaw, Van de Beek, Fred, Fernandes, Greenwood, Rashford, Cavani
Injury list: Paul Pogba (thigh), Eric Bailly (knock), Phil Jones (knee)