Highways England said the lorry is between J19 and J18.
One lane is still closed.
A Highways spokesman said: "There are 45 minute delays on the approach to this M1 incident (above usual journey times) spanning 5 miles back to J20.
"Average speeds on the approach to J19 are 11 mph. Please plan ahead if travelling in the region this morning."
Update from Highways England at 8,40am: "We have reopened all lanes J19 to J18 Southbound M1. The Emergency Refuge Area remains closed whilst contractors deal with the damage to the area."