The fires were discovered on Old Road, Tintwistle, on land near a quarry about 8.40pm, on Saturday, May 14.
A Derbyshire fire service spokesman said: “The fires involved an area of scrubland and grass about 100metres by 100metres which was well alight.
“Police were informed after information confirmed that a group of youths had been seen in the area prior to the 999 call to the fire service.”
Firefighters used beaters to extinguish the blaze and make the area safe.
The fire service also informed a park ranger of the circumstances.
Witnesses or anyone with information can call Derbyshire Constabulary on 101 or Crimestoppers in confidence on 0800 555 111.