He will take the summer off to pursue other interests and plans to return to advertising later this year.
His responsibilities will be assumed on an interim basis by Jane Wagner, a board director and the former chief executive of Saatchi & Saatchi Russia, who joined in February.
The agency is yet to appoint a replacement, but is understood to be in talks with Caspar Thykier, the former managing director of Shop, the agency that closed earlier this week.
Vick joined Duckworth Finn Grubb Waters, which was acquired by Freud exactly a year ago, in 1999.
His departure follows that of Dave Waters, the final remaining founding partner of DFGW. Waters quit as the executive creative director in November to launch a creative content consultancy with the production company executive Bertie Miller.