The fire broke out at about 10.20am on Monday at an address in Shrewsbury Road.
Two fire crews from Market Drayton were quickly on the scene.
Firefighters went into the house with breathing apparatuses and extinguished the fire within half an hour.
A spokesperson for Shropshire Fire and Rescue Service said the blaze involved an electric fire.
"Crews administered oxygen therapy to one casualty," the spokesperson said.
Earlier in the day fire crews in Shrewsbury dealt with a small fire in the kitchen of a house in the town.
Two fire crews from Shrewsbury and Wellington went to the house in Stretton Close after the alarm was raised just before 9am. They had the fire under control within 15 minutes.