The agency, which is owned by the Interpublic Group, is undergoing a management restructure and further redundancies are expected, according to sources.
Montgomery and Prior were only promoted to their most recent roles last February, appointments made by Patrick Smith.
In January, Smith was promoted to the post of global chief executive of FutureBrand. He is expected to lead the business following Montgomery's departure.
No one was available for comment at the time of publication.
Montgomery joined FutureBrand in 2003 as head of strategy from DBS Bank in Singapore, where she was vice-president of group branding and marketing. Before that, she spent two years at Interbrand.
FutureBrand has offices in 16 countries including New York, Rome and Paris. Clients include Procter & Gamble, Microsoft, Nestle and Nokia.