The airport claimed the cancellations are necessary for both safety and to ensure "as many passengers as possible" can catch their flight as planned.
Around 1,200 flights are scheduled to leave throughout the day. Airlines are contacting those who are affected by the cancellations. A "handful" of British Airways flights have reportedly been affected.
A spokesperson for Heathrow said: "We are expecting higher passenger numbers in today’s morning peak than the airport currently has capacity to serve, and so to keep everyone safe we have asked airlines to remove 30 flights from the morning peak for today only.
"We will work with airlines to get affected passengers rebooked onto other flights outside of the peak so that as many as possible can get away today, and we apologise for the impact this has on travel plans.
"We are working hard to ensure everyone has a smooth journey through Heathrow this summer, and the most important thing is to make sure that all service providers at the airport have enough resources to meet demand."
It comes weeks after the airport asked airlines flying from Terminals 2 and 3 to cancel 10% of their schedules due to problems with its baggage handling operation.