A man, woman and child were led to safety from their home after a fire was started outside the front door - blocking their way out.
The family discovered the blaze outside their home in Fleury Rise, Gleadless Valley, at 5am.
A sofa near their front door had been set alight.
The flames did not spread inside the house but they blocked the family's way out.
Firefighters extinguished the flames, led the family to safety and ventilated the property.
An investigation into the arson attack is now under way.
Group Manager Simon Dunker, of South Yorkshire Fire and Rescue, said: "Arson attacks like this are clearly reckless and have the potential to spread quickly and to cost lives.
"Anyone with information about people starting fires in their area should contact the police or call Crimestoppers."
Call South Yorkshire Police on 101 or Crimestoppers on 0800 555111.