The move by Heathrow affected around 5,000 passengers at Terminals 2 and 3 on about 30 flights.
It comes after images emerged on Friday of a huge pile-up of passengers’ luggage.
Heathrow hopes some airlines will respond to its request to reduce flights by consolidating their services, to enable passengers to still travel on Monday.
A spokeswoman for the airport said: “We apologise unreservedly for the disruption passengers have faced over the course of this weekend.
“The technical issues affecting baggage systems have led to us making the decision to request airlines operating in Terminals 2 and 3 to consolidate their schedules on Monday, June 20.
“This will enable us to minimise ongoing impact and we ask that all passengers check with their airlines for the latest information.”
It said it was “pro-actively consolidating a number of flights across affected airports”.
The aviation sector across Europe is experiencing “operational issues”, including air traffic control delays, staff shortages in ground handling and at airports, and increased times for identity checks of new recruits, easyJet said.
The airline has cancelled thousands of flights in recent months, particularly during school holidays at Easter and the half-term period, which coincided with the Jubilee bank holiday weekend.
Chief executive Johan Lundgren told reporters “I can’t tell you how many flights will be impacted” as “we need to work this through”.
He said: “It would be misleading for me to give any numbers today because we simply don’t know.”
Mr Lundgren said easyJet had previously planned to operate around 160,000 flights between July and September.
In May, the carrier expected its capacity to be at around 97 per cent of 2019 levels over that three-month period, but this has been reduced to 90 per cent.
EasyJet admitted there will be a “cost impact” from the disruption, and the amount of money it spends to operate each seat per kilometre excluding fuel will “exceed” previous guidance.
It said: “We believe that these capacity/cost impacts are a one-off this summer as we would expect all parties to build greater resilience in time for 2023 peak periods.”
Mr Lundgren said: “Delivering a safe and reliable operation for our customers in this challenging environment is easyJet’s highest priority and we are sorry that for some customers we have not been able to deliver the service they have come to expect from us.
“While in recent weeks the action we have taken to build in further resilience has seen us continue to operate up to 1,700 flights and carry up to a quarter of a million customers a day, the ongoing challenging operating environment has unfortunately continued to have an impact, which has resulted in cancellations.
“Coupled with airport caps, we are taking pre-emptive actions to increase resilience over the balance of summer.”
Ryanair, which has been largely unaffected by recent cancellations, announced it had added 200 “rescue flights” on its routes serving 19 UK airports until the end of September.