At 5.30am, a person was hit by a vehicle on the southbound carriageway between Junction 36 and Junction 35a.
Police have erected a screen at the scene, blocking the view of the crash from drivers on the northbound carriageway.
The road remains closed at 11.30am and South Yorkshire Police warn drivers to avoid the area, as officers investigate the crash.
A diversion is in place and there are still severe delays of about 20 minutes, building back to Junction 38.
The AA reports that traffic is moving at an average speed of 10mph.