Witsel, who played a full part in Saturday's 5-0 win over Fortuna Dusseldorf, underwent oral and facial surgery at Klinikzentrum Nord Hospital over the weekend.
The Belgium international has been discharged from hospital but will miss at least four matches ahead of the mid-season break, starting with Tuesday's Champions League clash with Slavia Prague.
Witsel has suffered a facial injury and will be out for the rest of the year.— Borussia Dortmund (@BlackYellow) December 9, 2019
Wishing you a speedy recovery, Axel! 💪 pic.twitter.com/k5KKQ7drrp
"Witsel will sadly be out for the rest of this year," BVB boss Lucien Favre confirmed at Monday's pre-match news conference.
"I was told about this yesterday morning. We could not speak to him. He was in hospital.
"But there is one positive thing - he's already back home. We can't change it now. It's a shame for him, a shame for us. He's one of the most important players for us."
Asked to provide more details on the injury, Dortmund media director Sascha Fligge said the midfielder "fell awkwardly at home".
Witsel has scored three goals in 21 appearances for Dortmund this season.