Wright, who left the agency last week, will not be replaced directly.
Instead, a team of three managing partners will run the agency.
Phil Nunn, the agency's director of digital and direct, has been promoted to managing partner to lead the agency alongside Robert Ffitch and Neil Hurman.
Wright, who joined MG OMD in 1999 from HHCL & Partners and was made the managing director in 2002, left the agency suddenly and without a job to go to after a restructure instigated by the OMD UK group chief executive, Nick Manning.
MG OMD recently broke into the top ten media agencies based on billings, but it has had a slow new-business year and suffered the recent loss of its More Th>n account to Universal McCann.
Wright said she would spend six to 12 months with her family before deciding whether to seek a move back to an agency.
Manning commented: "In the immediate term, the agency will be led by Robert, Neil and Phil, and I will help them determine the future direction and strategy for MG OMD. I would like to thank Alison for the contribution she has made to the agency."
Ffitch was a founding member of the Manning Gottlieb Media management team. Hurman joined the agency last year after leaving Mirror Group Newspapers and Nunn also arrived in 2003 after running Optimedia's interactive division.