In comments which were widely condemned, the 80-year-old Meisner last month told members of the conservative Neocatechumenal Way Catholic group: "Each of your families is easily worth three Muslim families for me."
Meisner has been archbishop of Cologne since 1989. "The Holy Father has accepted the renunciation," the Vatican said in a statement.
Meisner was one of the cardinals who took part in the conclave that elected Pope Francis on March 13 last year but has now lost the right to elect a future pope because he has reached the age threshold of 80.
All bishops are asked to submit their resignations when they reach the age of 75, although it is then up to the Vatican when to accept them.