North Yorkshire Fire Service said crews from Danby and Whitby had been dispatched to the property in the village of Glaisdale shortly before 5.20pm yesterday.
A spokesman said the fire had caused damage to the cooker top, extractor hood and ceiling, as well as smoke damage to the rest of the kitchen.
"The fire was extinguished by occupant using a fire blanket and dry powder extinguisher," he said. "Fire crews carried out an inspection using a thermal imaging camera. The cause is believed to be a pan left unattended."
The alarm was raised when smoke detectors fitted to the property began to sound, the spokesman added.