Crews were called to the scene on Raikes Road at around 9.30pm yesterday evening after a smoke alarm sounded at the property.
Firefighters found the property was heavily smoke logged and used a fan to clear the terraced house of smoke.
A spokesman for the fire service said: "We were called out to a fire where a plastic chopping board had been left on top of a hob.
"The house was filled with smoke.
"The mother did all the right things - her smoke alarm worked, she turned the power off to the cooker and waited outside for us to arrive.
"There was very little damage but it just shows how important smoke alarms are and if your cooker is not in use, it's a good idea to turn it off at the mains.
"The occupants of the house were treated at the scene by paramedics."
The mother and the child did not suffer any serious injuries.