The absence of goalkeeper Gulacsi is a further blow to Leipzig in Belgium with forwards Yussuf Poulsen and Dani Olmo already sidelined by injury.
With Marsch also out, assistant coach Achim Beierlorzer will be in charge in Belgium, the club has said.
With one point from their first four European games, Leipzig are bottom of their group and must beat Club Brugge to keep alive hopes of finishing third to qualify for the knock-out rounds of the Europa League. Marsch and Gulacsi have both tested positive despite being fully vaccinated, as is the entire Leipzig squad and staff.
In a press release Tuesday, the Bundesliga club also revealed that they “will soon begin carrying out booster vaccinations”.
Marsch’s assistant coach Marco Kurth also misses the away match after a positive case of the virus in his immediate family.