Robben picked up a minor muscular problem while away on international duty with Netherlands and missed the 1-0 Bundesliga defeat to rivals Borussia Dortmund at the weekend, while Javi Martinez sustained a hamstring injury against Augsburg last month.
The duo resumed training on Monday and were thought to be in line for a return in the Group D contest, but Bayern confirmed the pair will stay behind in Munich rather than make the trip to Russia.
Vidal, who picked up a knock while on Chile duty during the international window, has also been omitted from the squad.
Bayern were already without the services of goalkeeper Manuel Neuer (calf) and Kingsley Coman (leg).
Carlo Ancelotti's men have already qualified for the knockout stages heading into the game against Rostov, having collected nine points from their opening four Group D fixtures.