"We couldn't talk to him yesterday (Sunday) because he was in intensive care in hospital," said Dortmund coach Lucien Favre, while a club spokesman said Witsel fell at home but gave no further details.
"He won't be able to play for the rest of the year, but he is already at home," added Favre.
"It's a shame for him and us, he's an important player. Hopefully he is back as soon as possible."
The 30-year-old Witsel will miss Dortmund's final Champions League group game at home to Sparta Prague on Tuesday.
They must better Inter Milan's result against Barcelona at the San Siro in order to reach the last 16.
The Belgium international will also be sidelined for the next three league games. Dortmund are third in the table, five points behind Bundesliga leaders Borussia Moenchengladbach.
Witsel played in Saturday's 5-0 thrashing of Fortuna Duesseldorf and has featured in all five Champions League group games this campaign.