One protester said they were campaigning against a third runway and would stay there for as long as possible.
A Heathrow Airport spokesman said: 'A group of people have breached the airport perimeter fence and are currently staging a protest on the northern runway.
'We are working closely with the police who are dealing with the incident. The southern runway remains open. Our priority remains to ensure the safety of the airport community, including passengers, employees and protesters'.
A video posted online appeared to show several activists chained together and being spoken to by a police officer.
The officer told them: 'As a consequence of you being here, you are causing severe disruption and it will be in the millions of pounds because it will take us a while to remove you.
'The cost will be in the couple of millions. The airport will attempt to make a civil recovery.'
He added: 'There are international flights now being diverted.'
Earlier this month a long-awaited report recommended that a new runway should be built at Heathrow rather than Gatwick.
After three years of investigation, the Airports Commission said Heathrow was best placed to provide 'urgently required' capacity, but environmentalists warned that building a new runway there will make it harder to reduce air pollution and climate change emissions.
Ella Gilbert, one of the activists on the runway, said: 'Building more runways goes against everything we're being told by scientists and experts on climate change.
'This would massively increase carbon emissions exactly when we need to massively reduce them, that's why we're here.
'We want to say sorry to anyone whose day we've ruined, and we're not saying that everybody who wants to fly is a bad person.
'It's those who fly frequently and unnecessarily who are driving the need for expansion, and we cannot keep ignoring the terrifying consequences of flying like there's no tomorrow.
'No ifs, no buts, no third runway. And we mean it.'
