Priority shareholders made the proposal ahead of Heineken Holding's AGM on April 21, as Hoyer, at the age of 71, is set to retire.
Kwist, who is currently director of Greenfee and L’Arche Green, has experience in brand management consultancy, marketing and communication.
For ten years Kwist worked for Procter & Gamble in a number of management positions.
Hoyer has served as a member of the board of directors since 1972.
In a statement Heineken said: "Mr Hoyer is due to retire by rotation and, in view of his age, will not be proposed for reappointment.
"In that capacity he made an invaluable contribution to the achievement of Heineken Holding N.V.’s primary objective, namely to safeguard the long-term independence, continuity and stability of the Heineken group, for which the board of directors thanks him most sincerely."