Crews from Alfreton and Ashfield were called to Main Road in Pye Bridge at around 4am.
A Derbyshire Fire and Rescue Service spokesman said: "The fire was in the kitchen of a house.
"A woman was treated for smoke inhalation at the scene and crews rescued a cat from the property.
"Gas and electricity supplies were isolated and the gas board also attended this incident.
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For advice on staying safe in your kitchen, visit www.derbys-fire.gov.uk/keeping-safe/common-fire-prevention/kitchen