The pressure group, which wants an end to oil and gas extraction and use, said seven of its supporters were detained at two locations on Heathrow's perimeter road at about 9:00 am (0800 GMT).
London's Metropolitan Police said 10 activists were held for "conspiracy to interfere with key national infrastructure" and taken into custody.
Seven were arrested at Heathrow and three more at "other locations", the force said, adding that they recovered cutting gear and glue during the operation.
The activists were believed to be trying to get through the airport's perimeter fence, the Met added.
"Doing so would have led to the suspension of flight operations causing a major impact to international aviation," a statement said.
A Heathrow spokesperson said operations were not affected because of "swift action from the police and airport colleagues".
Heathrow, Europe's busiest airport in terms of passenger numbers, obtained a court injunction this month barring anyone from entering on its grounds "in connection with Just Stop Oil" or any other environmental campaign.
People breaching the injunction face up to two years in jail.
Injunctions were also issued for three other UK airports, as Just Stop Oil threatened to engage in action "at airports across the country" unless their demands were met.
Just Stop Oil wants the UK to halt new oil and gas licensing -- which the new Labour government has said it will do -- and to work on a fossil fuel treaty with other countries to end all oil, gas and coal extraction and burning by 2030.
- 'Oil kills' coalition -
JSO was one of seven groups that planned to or caused disruption at airports across Europe on Wednesday as part of "Oil Kills", a coalition of groups from 10 countries in Europe and North America demanding an end to oil and gas use.
The countries which saw protests included Germany, Norway, Finland, Spain, Switzerland and Austria.
At Germany's Cologne-Bonn airport, activists glued themselves on the runway on Wednesday morning, with flights grounded briefly before resuming.
At Vienna airport, four activists poured an orange substance in one of the airport's halls, holding signs that read "Oil kills".
Two other activists inside a Rome-bound plane refused to sit down before take-off and made a speech against climate change, delaying take-off, according to Last Generation Austria.
One of them was dragged out of the plane, the group said.
In Norway, around 12 activists blocked the runway at Oslo airport.
The protest organisers are part of the A22 Network of groups committed to non-violent climate protests, which said it was planning to disrupt airports in several countries in the coming months.
Protests were planned in Britain, Austria, the Netherlands, Switzerland, Canada, United States and Norway, UK-based activists from the alliance told AFP earlier in July.
Global aviation is responsible for around 2.5 percent of global carbon emissions, more than the annual carbon footprint of Brazil and France combined.
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