Two appliances and crews from Aylesbury attended.
The fire, caused by the washing machine, was in the kitchen of a two-storey building.
The firefighters provided immediate emergency care to one woman and one man, treating them for the effects of breathing in smoke, before handing them into the care of South Central Ambulance Service.
The firefighters used two sets of breathing apparatus, one hose reel jet and positive pressure ventilation to clear smoke.
They removed the washing machine into the rear garden of the property.