Passengers urged him to sit down and asked the crew to get him off the plane.
Mr Masters said: "I would like to thank all the well wishes I have received since Monday evening".
Airport and Aer Lingus airline officials said that a morning flight to Dublin had to be delayed by almost two hours after a ticketed passenger got up to make a speech about the climate as the plane prepared to take off.
On Thursday, 18,000 passengers were due to arrive or depart from the airport, with 286 flights scheduled.
The flight finally took off after 11 a.m. local time.
Extinction Rebellion led protests around the world as thousands of people took to the streets in NYC, London, Paris, Berlin, Sydney, and 55 other cities. Some had glued themselves to the floor, the paper said.
Videos showed the man, identified by the group as para-athlete James Brown, lying on the British Airways aircraft for over 20 minutes as authorities attempted to help him down.
Extinction Rebellion's colourful protests have managed to attract a mass following since its creation a year ago by United Kingdom academics studying the effects of harmful carbon emissions on Earth.
"We need to encourage people to fly less", the woman said.
In a live-streamed video posted on Facebook, Brown told followers that protest was "for my kids, for everybody's kids, for all the young people who face a horrendous future". At that point, the man remained sprawled on top of the plane.
United Kingdom media identified that person as 2012 London Paralympic Games cycling bronze medallist James Brown.
Later, answering questions about his backing for the protests, he added: 'We have to understand the passion and the motives of those that have taken part in the protests all over the country.
A protester is arrested after refusing to sit down on a flight to Dublin.
Witnesses reported "an extraordinary number of police officers" at the terminal as demonstrators try to emulate protesters who cancelled more than 1,000 flights as they condemned police brutality in Hong Kong. Authorities said they would deal with activists "robustly but proportionately".
Metropolitan Police deputy assistant commissioner Laurence Taylor said "some interesting attempts" had been made to disrupt flights. "The consequences of committing offences at airports are serious; individuals breaking the law are being, and will continue to be, arrested and prosecuted where appropriate".
Numerous climate change activists were arrested at London City airport as part of ongoing protests.
The Labour leader spoke out after demonstrations in the capital and other parts of the United Kingdom escalated into a three-day Hong Kong-style protest.