Camden Council leader Georgia Gould said the Taplow building would be “temporarily decanted” to allow “urgent fire safety works” to take place.
The council had already announced it would immediately begin preparing to remove cladding from five towers on the estate discovered in checks following the fire in north Kensington which killed at least 79 people.
In a statement on Friday evening Ms Gould said firefighters and council officials had inspected the estate on Friday.
She added: “Together we decided that the Taplow block needs to be temporarily decanted while we undertake urgent fire safety works so that residents can be fully assured of their safety.
“This means that we need to move residents from their homes and into temporary accommodation.”
Ms Gould said it was expected the work would take three or four weeks, adding: “We realise that this is hugely distressing for everyone affected and we will be doing all we can, alongside the London Fire Brigade and other authorities, to support our residents at this difficult time.
“The Grenfell fire changes everything - we need to do everything we can to keep residents safe.”
It came as four more victims of Grenfell Tower were formally identified, taking the known victims of the fire to nine.
Scotland Yard also revealed manslaughter charges are being considered by detectives investigating the blaze in the tower in west London, which had failed fire safety tests.