Millard-Beer will be responsible for growing the brand consultancy's business in these regions, as well as looking at the opportunities for establishing local Interbrand operations.
He joins from the public relations firm Fleishman-Hillard, where he was a director. His prior experience includes setting up and managing the Middle East and North Africa network for the public relations firm Porter Novelli.
Rune Gustafson, chief executive of Interbrand UK, said: "Matthew is joining us at a time when our international work needs a leader to consolidate our position and ensure that we continue to deliver excellent, award-winning work in these key markets."
Interbrand was established in 1974 and has offices in 25 countries. It works for brands including BMW, Barclaycard and Samsung.