The captain was reportedly seen entering the aircraft’s toilet on flight EZY6938 as the first officer landed the plane in Scotland’s capital in the early hours of Sunday morning.
Five fire engines and two ambulances arrived at the scene and the captain was treated by paramedics, a witness said.
They told the Daily Record: “The captain had been seen going into the toilet and not coming out. The plane was met on the runway by five fire engines and two ambulances.
“After landing the co-pilot announced on tannoy that the emergency response was due to the captain taking ill.”
A spokesperson for Easyjet told the newspaper: “easyJet can confirm that flight EZY6938 from Heraklion to Edinburgh on 12 June requested an expedited landing due to the Captain becoming unwell while on approach to Edinburgh.
"The First Officer landed the aircraft in line with standard operating procedures and the Captain was met by paramedics on arrival as a precaution.
“The safety and wellbeing of our passengers and crew is always easyJet’s highest priority."
The Standard has contacted easyJet for further comment.
It comes as travellers continue to face chaos at Britain’s airports, with dozens of flights axed and long queues reported for security.
EasyJet axed 20 flights from Gatwick last week due to strike action in Italy including departures to Bologna, Milan, Naples, Rome and Venice.
The low-cost airline has already cut some 40 flights a day for the rest of the month in a bid to avoid last-minute cancellations for passengers.
Airlines have struggled to cope with a surge in demand prompted by the end of Covid travel restrictions, with many forced to rapidly recruit staff after laying off large numbers of employees during the pandemic.
Tory MP Huw Merriman, chairman of the Commons Transport Select Committee, said last week that the Government should have taken more action to prevent travel disruption.
“I think there’s been a failure to understand that you can’t just flick a switch and expect the aviation industry to restart,” he told the BBC.
“They only had the full go-ahead on March 18. There’s a requirement for them to operate 70% of their slots, otherwise they could lose them.
“So, effectively, the Government and Parliament have told them to restart at those levels, but it can take three months to get staff recruited and through the vetting process.”