The 32-year-old midfielder is expected to remain sidelined until at least the end of February after aggravating a groin and adductor problem, an issue understood to be separate from his previous injury.
Can has featured 14 times in all competitions this season and scored three goals, making his absence a significant loss for Dortmund's leadership and experience in midfield and defence.
Dortmund face Wolfsburg at the Volkswagen Arena in a key Matchday 21 encounter, with the visitors currently sitting second in the Bundesliga table. Kovac's side have been in impressive domestic form, putting together a 13-match unbeaten league run and closing the gap to leaders Bayern Munich to six points.
Can's injury adds to a growing list of defensive concerns. The premature end of Aaron Anselmino's loan and a separate injury to Filippo Mane have already stretched Dortmund's backline. As a result, several young players have been included in the matchday squad, including highly rated 18-year-old defender Luca Reggiani, who could be handed a senior debut against Wolfsburg.
Despite these challenges, Dortmund remain confident of maintaining their strong title push. The club's consistent performances this season have kept them firmly in the race, and there is still hope internally that Can could return in time for the crucial Der Klassiker clash against Bayern Munich later in February if his recovery progresses as planned.
With momentum on their side and pressure building at the top of the table, Dortmund will be aiming to extend their unbeaten run and cope without their captain as they chase another important Bundesliga victory.