“We have decided to transition our business to other suppliers over time,” McDonald’s said.
In February, Heinz was purchased in a $28bn (£17.3bn) takeover.
McDonald’s said that it would work with Heinz “to ensure a smooth and orderly transition of the McDonald’s restaurant business”, which has 34,000 restaurants around the world.
Mr Hees took over after Heinz was bought by Warren Buffett’s Berkshire Hathaway and Brazilian investment fund 3G Capital. Burger King is controlled by 3G Capital.
McDonald’s uses the ketchup at many stores around the world, though only in Pittsburgh and Minneapolis inside the US.
“As a matter of policy, Heinz does not comment on relationships with customers,” the ketchup-maker said.