The Dutchman, injured in a Euro 2016 qualifier against Iceland last month, had been hoping to make his comeback in London.
"For Robben this trip is too soon," Bayern, who left on Sunday evening to avoid travelling through the English capital's Monday traffic, said in a statement.
Fellow winger Kingsley Coman, however, was included, with the Frenchman having missed Saturday's 1-0 win over Werder Bremen after being injured while playing for France's Under-21 team last week.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Bayern are top of Group F with a maximum six points while Arsenal are languishing in last place after two defeats.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
