Both the clubs said the move was to help the other employees financially during the coronavirus crisis.
Bayern players will be taking a 20% pay cut, while Dortmund players will "waive part of their salaries".
Union Berlin announced they will go entirely without their wages.
La Liga: Atletico, Espanyol join Barca in cutting wages
In La Liga, Espanyol and Atletico Madrid joined Barcelona in announcing they will apply temporary pay cuts to their players as a result of the economic impact.
Meanwhile, other Spanish first division clubs are expected to follow suit in the coming days, with Real Valladolid the only one so far to have announced that none of their staff will be subject to cuts.