Nick Barton, BAA's commercial director at Stansted, told BBC Radio 4 he hoped the airport would be able to "recover quite well" from the impact of the protest, but admitted delays were likely for the rest of the day.
Passengers due to travel on Monday are being advised to contact their airline before setting out.
Ryanair called for an investigation into why BAA had failed to keep the airport "secure and open", saying the disruption to passengers was "unacceptable".
Plane Stupid began its protest at 0315 GMT and said it was intended to draw attention to CO2 emissions from the aviation industry.
Mr Barton said he believed the protesters had arrived in a number of vehicles including an old fire engine.
One of the activists taking part, Lily Kember, 21, said they had then forced their way in using bolt-cutters.
Plane Stupid apologised for disrupting individual journeys
The BBC's Stephen Chittenden, at Stansted, said they had brought concrete blocks and 6ft-high security fencing with them and erected a "stockade" about 50m (164ft) from the runway. They then chained themselves to the fencing.
The runway was closed for about two hours and reopened at 0810 GMT after police removed the protesters.
Flights resumed immediately, but long queues quickly built up in the terminal.
Passengers were handed printed sheets explaining the reasons for the delay and police helped staff to deal with queries.
Anita Kelleher had been due to fly to the Irish Republic to attend her father's funeral, but her flight was cancelled.
"His funeral is tonight, the Rosary is tonight. I've missed being at my dad's Rosary tonight and I'm heartbroken," she told the BBC.
Protester Lily Kember says "people need to take responsibility" over climate change
Another passenger, Vivienne Brinton, had been due to fly to her second home in France.
She said: "I suppose people will have some sympathy with the protesters, but in the modern world we live in, people want to travel."
Nicola Hilda and a friend had been supposed to travel to Bremen in Germany for a day trip, but their flight was also cancelled.
"We've saved up for it for months and months and we're just thoroughly disappointed," she said.
BAA said it would investigate the break-in and, where necessary, learn lessons from it.
"We respect people's right to protest within the bonds of the law," it said in a statement.
"However any unlawful or irresponsible behaviour aimed at disrupting the smooth operation of the airport is unacceptable."
Prime Minister Gordon Brown's spokesman told a media briefing: "Of course everybody has a right to protest, but people also have a right to be able to travel without unnecessary hindrance."
In October controversial plans for an expansion of Stansted airport were given the go-ahead by the government.
Airport owner BAA wants to increase passenger numbers from 25 million to 35 million a year and flights leaving the airport from 241,000 to 264,000 a year.
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