Police said four arrests were made after a female pedestrian in her 50s was hit by the vehicle, previously reported as stolen, before it hit two parked cars and ploughed in to the house on Park View, Brierley.
The HGV was being followed by a police vehicle just before the crash, South Yorkshire Police confirmed. A referral has been made to the Independent Office for Police Conduct (IOPC).
A police spokesperson said: “At around 1.40pm, a HGV, previously reported as stolen, was travelling along Common Lane, towards Grimethorpe, when an officer in a marked patrol car, travelling in the opposite direction, turned round to follow the vehicle.
“The HGV then travelled on to Park View, where it was in collision with a pedestrian, a woman in her 50s.
“The vehicle then hit two parked cars before colliding with a house on the road and coming to a stop. The woman was sadly pronounced dead at the scene.
“While formal identification has not yet taken place, her family have been informed and are being supported by specialist officers.”
Yorkshire Ambulance Service said three people were taken to the major trauma unit at Sheffield’s Northern General Hospital following the crash. No details of their injuries were released.
The man driving the vehicle was also taken to hospital with minor injuries, police said.
The spokesperson added: “Four men have been arrested in connection with the incident and remain in police custody at this time.
“Police remain in the area, as enquiries are carried out and Park View is expected to remain closed for the evening.”
A spokesman for police watchdog the IOPC said: “We were notified by South Yorkshire Police about this incident at around 3pm today and sent our investigators to the scene and police post incident procedure to gather information and assess the level, if any, of our future involvement.”
South Yorkshire Police appealed for witnesses to the crash to call 101.