His departure comes at a time when the agency's grip on the Toyota account, which it has held since 1993, is becoming increasingly tenuous.
In July, Saatchis lost the £50 million Toyota GB account to its fellow roster agency CHI & Partners. CHI picked up its first piece of Toyota business in 2004 with the launch of the Aygo. Since then, it has also won the pan-European Corolla and Yaris accounts.
Wright joined Saatchis in 1992 and has worked predominantly on the Toyota account. He was promoted to managing director of the agency in 2005.
He moved to his current role in August 2006, after Saatchis decided to restructure its senior management team in a bid to stabilise the agency and cement client relationships, while improving its new-business record.
Jim O'Mahony, the chief executive of Saatchi & Saatchi China, Russia, India and Brazil, said: "John is leaving at the end of August to take a career break and spend time with his family. I know this is not a decision John has taken lightly. Saatchis has been his home for more than a decade and he has played a huge role in shaping its culture, particularly over the past few years.
"At some point, however, everyone has to take on new challenges."
Last month, Campaign revealed that Publicis Groupe was aligning Saatchis with Fallon under a new mini group structure, which will be headed by the Fallon founding partner Robert Senior.