They said that three men, who are aged 19, 23 and 24, remained in custody on Sunday afternoon and that police are working with the fire service to establish if this incident is linked to the larger blaze.
There were two separate fires on Ilkley Moor which blazed from Saturday until Sunday.
The first was near Bingley by the Dick Hudson's pub and this blaze was extinguished on Saturday.
A spokesperson for West Yorkshire Police said the fire was now believed to be 'under control'.
They said: "The fire service are continuing to tackle the blaze and members of the public are advised to avoid the area.
At one point 70 firefighters were tackling the fire on Moorland above Ilkley.
Emergency services used a helicopter for water drops to get the blaze under control.
There have been no reports of injuries and no homes were evacuated but those living closest to the Moor were given the option of alternative accommodation by Bradford Council on Saturday night.
West Yorkshire Fire and Rescue Service said on Sunday afternoon that they still have 12 fire engines in attendance using three large jets.
More on the Ilkley Fire: