Lowe, who launched The Red Brick Road in March 2006 with Tesco as its founding client, remains a shareholder.
The agency will continue to be managed by the remaining partners Paul Weinberger, Paul Hammersley, David Hackworthy, Sam Cartmell and Jason Lawes.
Although Lowe, 68, is understood to be reluctant to retire completely, sources at the agency indicated that he was unlikely to take another full-time advertising agency role.
Lowe launched The Red Brick Road alongside his former Lowe London colleagues Weinberger and Hammersley after landing the Tesco creative account.
While Lowe had a close relationship with Tesco, particularly with its chief executive, Sir Terry Leahy, Weinberger has been leading the account for some time and will continue to manage the business in Lowe's absence.