After winning the account in 2013, the agency had informed the client earlier this year that it would not be repitching ahead of a statutory review which is imminent.
The decision is not related to the agency winning American Airlines' global ad account last year.
It is understood a pitch process will take place in the New Year, run directly by Turkish Airlines global advertising manager, Rafet Fatih Ozgur.
In February CP&B created a global campaign for Turkish Airlines which featured Ben Affleck and Jesse Eisenberg in spoof tourism ads for Gotham City and Metropolis, the cities featured in the blockbuster movie Batman v Superman: Dawn of Justice.
Richard Pinder, the agency's UK and international chief executive, said: "We’ve had an amazing three-and-a-half year journey and done some exceptional work that we’re very proud of.
"Together we’ve transformed Turkish Airlines into a world class consideration brand. However, over the last 12 months, circumstances on the account have become increasingly untenable for our people.
"Some time ago I informed Turkish Airlines that when they chose to conduct their statutory review we would not participate – so today it’s time to say goodbye. We wish Turkish Airlines nothing but the best."