Highways England has reported the motorway has been shut between junction 36, for Tankersley, and junction 37, for Barnsley.
It said the road was closed in both directions, and that traffic was being diverted,
Northbound traffic is being diverted from J36 - via the A61 westbound, the A616, the A629 northbound and the A628 eastbound - to return at J37.
Southbound traffic is being diverted via the A628 westbound, the A629 Southbound and A616 eastbound - to leave at J37 and return at J35a.
Highways England said on social media: “Delays are likely on the approach to this closure, with additional journey times also expected on diversion routes.”
Delays are building on the approach to the closure - currently 90 minutes southbound and 60 minutes northbound above normal journey times.
Motorists are being encouraged to use the M18 and A1M, to avoid the area.