Highways England has said the road is closed in both directions between Junction 22 at Denshaw and J24 near Huddersfield.
"Any traffic within the closure is soon to be turned and released," the authority has said. "The emergency services are working at the scene."
West Yorkshire Police has said the closures are likely to be in place for several hours, and is urging motorists to avoid the area. Diversions are in place.
"Motorway in both directions will remain closed whilst we deal with this incident," the force said in a statement.
"Diversions are in place and the closure is likely to be in place for several hours."