The fire service said it had been working to protect properties including Coastguard Cottages, Mount Pleasant Farm and Cliff House Holiday Park, but all had been evacuated overnight.
Up to 200 caravans are being prepared for evacuation, but the exact number of people affected is not known.
The fire comes as the UK Health Security Agency has issued an amber heat-health alert for the East Midlands, the East, South East and London.
The Environment Agency (EA) announced on Wednesday that the East of England, including Suffolk, was part of an area in England where drought was declared.
Droughts bring with them a high risk of wildfires, the EA warned.
Much of the area is a nature reserve owned by the National Trust, which said it was assisting firefighters.
The area is also close to the RSPB Minsmere nature reserve.
Both National Trust Dunwich Heath and the nature reserve have been closed.
It asked people to avoid Westleton Heath, Mount Pleasant, Westleton Walks and the main bridleway from the entrance road towards Dunwich.
The fire service said crews are using equipment including off-road vehicles, drones and quad bikes.
“Members of the public are advised to avoid the area and keep roads clear for emergency vehicles,” it said.
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