The agency has put Paul Smith, its European creative director, into the post until a permanent replacement has been hired.
In a statement the agency claimed that "no other personnel changes in the creative department are envisaged".
It is understood that Dunn, 42, is taking legal advice and is considering action against the agency. He refused to comment on his departure.
The agency's decision is not altogether unexpected - Dunn was not among the senior executives promoted to a group role following the removal of Simons by the European chairman Mike Walsh. The decision to remove Dunn was taken by the chief executive, Paul Jackson, who replaced Simons in April.
Jackson said: "We have some tremendous talent in the creative department and an enviable client list. I shall be seeking a creative director who can bring the two together in the most productive way for Ogilvy."
It also follows last month's announcement that O&M had recruited Dennis Lewis as a creative director as part of what the agency claimed would be a pair of heavyweight creative signings.
Lewis was a partial replacement for Paul Belford and Nigel Roberts, who quit earlier this year to join Abbott Mead Vickers BBDO. At the time, Dunn claimed this would allow him time to step back from the day-to-day running of the creative department.
Dunn has been at O&M since December 1999 and was one of Simons' first appointments as chairman.
He was hired as a joint executive creative director, but the agency failed to find a copywriting partner for him, so he took sole command of the department.
Before joining Ogilvy, Dunn had worked as the head of art at Lowe Howard-Spink and as the creative director at Wieden & Kennedy in Portland, Oregon.
He was most awarded while at Leagas Delaney, where he partnered the now chief executive, Tim Delaney. Here he worked on clients including Adidas and Nationwide.