The Netherlands international is being plagued by physical problems and has been left out of the Bavarians' match squad for Tuesday's game
The Dutchman picked up a muscular problem in Bayern's Bundesliga win over Wolfsburg and consequently missed this weekend's victory over Werder Bremen.
The Bavarians were initially hopeful that Robben would be match fit in time for the trip to Belarus, but they have now announced on their official website that the winger's injury is still causing him too much trouble.
Bayern will be looking to maintain their perfect record in the Champions League after beating Valencia 2-1 on matchday 1.
BATE, meanwhile, recorded a 3-1 win over Lille in their Group F opener.
Tuesday's encounter in Minsk is scheduled to kick off at 20:45CET.