Four were treated for smoke inhalation and one was taken to hospital with burns, Devon and Somerset Fire and Rescue Service said.
The gorse fire, which began at about 13:45 BST, has engulfed a large area of dry heath-land on Woodbury Common.
Twenty fire engine crews were sent to tackle the flames that were fanned by high winds.
The fire is being fought on a number of fronts and a police helicopter has been deployed to help survey the scene.
Chief Fire Officer Lee Howell said it was a "very difficult incident" and his teams were struggling with wind direction and a lack of water supplies.
He said: "It's a very, very large area - at the moment it's difficult to quantify and there is a fire front on a number of different parts of the common - and so our resources are being targeted to bring that under control in a number of different areas."
He added that firefighters will be at the scene overnight and into the early hours of Monday morning.
The nearby Woodbury Park Golf and Country Club has been evacuated as a precaution.
Smoke can be seen for miles around and the public have been advised to avoid the area.
Five firefighters have been injured while tackling a blaze on common land near Exeter.