The band said the show at the Johan Cruijff Arena would be rescheduled and that they were "deeply sorry".
Sir Mick, 78, added in a message to fans: "Thank you for your patience and understanding."
The band are currently on their Sixty tour, where they had planned to play 14 shows in 10 European countries.
Tickets for the original show will be honoured for the new date once the show is postponed.
The Stones had already played three of their tour dates, including one in the UK at Anfield in Liverpool.