Three fire engines attended and the road was closed from the A689 slip road onto the A19, before reopening at around 12pm.
Cleveland Police have said one woman sustained injuries which are not believed to be life threatening.
The North East Ambulance Service dispatched one paramedic crew and took the patient to Stockton’s University Hospital of North Tees.
The incident happened at around 9.35am.
Cleveland Police said earlier on Wednesday: “Police and other emergency services are on scene at a two-vehicle collision involving a Ford Fiesta and a HGV which took place around 9.35am on the A19 northbound near Elwick.
“The road will be closed from the A689 slip road onto the A19.”