The German champions were already without Luis Díaz and Jamal Musiala for Saturday's 2-2 draw with Borussia Dortmund, before the Klassiker brought further problems for their attacking options.
Ismael Saibari and Serge Gnabry were both forced off during the first half, while Michael Olise also had to leave the field late in the match.
The injuries have raised questions about whether Bayern Munich will need to strengthen their squad during the winter transfer window. Dreesen, however, was reluctant to commit to any plans when asked about the possibility after the draw.
“No, I don't think we need to bring anyone in. Lucho is on a good path, Jamal will be back soon. You shouldn't commit yourself to anything too early,” the Bayern chief executive told Sky.
Dreesen had already described a discussion about winter business as premature, suggesting the club want to assess the situation once more is known about the injured players and the expected returns of those already sidelined.
The scale of the latest setbacks could nevertheless complicate that approach. Saibari and Gnabry both suffered injuries against Dortmund, while Olise's condition also required assessment after he was substituted.
Bayern subsequently confirmed that Saibari had sustained a syndesmosis ligament tear in his right ankle and had undergone surgery. Gnabry was diagnosed with a muscle injury in the back of his left thigh. The club did not provide a return date for either player in its initial update.
Olise's situation remained less clear, leaving Bayern hoping his absence would be shorter than those of his team-mates.
The timing is particularly challenging for Vincent Kompany's side, with a demanding schedule approaching. Bayern travel to face Atlético Madrid in the Champions League on Tuesday before the calendar moves towards the decisive stages of the season.
Díaz and Musiala returning would provide some relief, but the latest injuries have exposed the limits of Bayern's options in attack. The club have a squad full of established stars, yet further long-term absences could leave Kompany short of alternatives across several positions.
Dreesen's comments indicate that Bayern are not ready to make a commitment to January recruitment. Much will depend on the recovery timelines of the injured players and whether the expected returns of Díaz and Musiala arrive as planned.