Shropshire Fire & Rescue Service scrambled appliances from Telford Central and Tweedale fire stations to the blaze in Burtondale, Brookside, at 6.49am on Friday.
The fire service said there was a "severe fire involving first floor of two-storey end of terraced property."
Crews wearing breathing apparatus were sent to the scene, where they used two hose reel jets and covering jet as neighbours watched on.
Fire control confirmed that the fire was ongoing at 9.45am.
Speaking at the scene, one fire officer stressed "the importance of having a smoke alarm as this family didn't and they were very lucky to come out with just smoke inhalation".
A Shropshire Fire & Rescue Service spokesperson added: "We were called at 6.50am today to Burtondale in Brookside, Telford. Three crews from Telford and Tweedale are in attendance. The fire involves the first floor of the property.
"Six firefighters are wearing breathing apparatus and using two hose reel jets and a covering jet to tackle the fire which is still in progress."
Officers from West Mercia Police erected a small cordon at the house, which sites at the end of a small terrace of three, and said the family were safe and well following their ordeal.
Neighbours also expressed their relief that everyone had got out.
One neighbour recalled hearing voices as the family were escaping the house.
She said: "We just heard voices, we didn't see any flames or anything. I saw two fire engines come in to the car park.
"The main thing is that they all got out safely."
West Midlands Ambulance Service confirmed one ambulance was sent to the scene.