Emergency services were called to the A57 Mosborough Parkway at 1.23pm.
The road was closed while firefighters tackled the blaze, between Coisley Hill and Drakehouse.
Posting on Facebook, South Yorkshire Police said shortly after 2pm that there was '˜some disruption' but traffic heading into the city centre could now pass.
Police said the road was closed between Coisley Hill Roundabout and Moss Way Roundabout before reopening at 3.14pm.
They added that a family travelling in the vehicle escaped unharmed.