A red Toyota Yaris, a silver Peugeot 308, a red Ford Fiesta and a black Ford Kuga were involved in a collision between the Prince of Wales Road entrance and the exit for the Parkway markets at 8.20am.
The Yaris then struck the central reservation barrier.
A 32-year-old woman is believed to have suffered a medical episode at the wheel of the Yaris.
He was taken to hospital, where her condition yesterday was critical.
A South Yorkshire Police spokeswoman said: "She is not believed to have suffered any injuries due to the collision and no additional injuries to anyone else have been reported.
"The section of the Parkway where the collision occurred was closed throughout the morning while officers began investigating the circumstances that led to the incident."
Anyone with information should call South Yorkshire Police on 101.