Just Stop Oil said about 18 people gathered at the Kensington property holding placards and “made themselves heard by beating pots and pans”.
It is not known whether the prime minister or his family were inside at the time.
No 10 declined to comment on the incident.
The Metropolitan Police said those arrested have been taken to a number of central London police stations and remain in custody.
A statement issued by Just Stop Oil called the protest a “wide awake disruption”, with some of its placards reading “no rest for the wicked”.
The group highlighted its opposition to the prime minister’s decision in July to grant 100 new North Sea oil and gas licences.
It comes three months after Greenpeace supporters climbed onto the roof of Mr Sunak’s property in his North Yorkshire constituency.
Four people were arrested on suspicion of causing criminal damage and a public nuisance after scaling the house using ladders and ropes. A fifth activist was arrested on suspicion of causing a public nuisance.
The latest protest was staged on the eve of the COP28 climate summit, which is being held in Dubai.
Mr Sunak is expected to travel to the United Arab Emirates for the conference, along with King Charles III and leaders from around the world.