A family cat has apparently ignited a costly house fire in Adelaide after jumping on to the kitchen bench and turning on a stovetop burner.

Fire authorities extinguished the house fire when they were called to the suburb of Hillcrest on Tuesday night after passers-by heard a smoke alarm.

The Metropolitan Fire Service pointed the finger at the cat, who was the only living creature at home, after ruling out the possibility the ceramic stovetop suffered an electrical fault or was accidentally left on.

An MFS spokeswoman said it was likely the cat had jumped on to the stove, which could be turned on by pressing one button, and this then set fire to cereal boxes left on the benchtop.

The cat was unhurt but the fire caused $40,000 worth of damage after spreading from the stovetop to the ceiling.