Fire crews from Barnstaple, Lynton, South Molton, Bampton, Tiverton and Dulverton were sent to the scene.
The service said crews used a water bowser, hose jets and beaters to prevent the flames spreading.
The fire service said on social media on Tuesday it was working with Devon and Cornwall Police into the cause.
In a statement, it said: “We are issuing a warning to people after several fires have been started deliberately in the countryside since Christmas.
“A period of exceptionally dry and windy weather has contributed to the spread of uncontrolled wildfires in the West Anstey Common area and one at Meldon Common, Chagford.”
The BBC has contacted police for more information.