The road has now been closed in both directions between junction at B6387 Gamston and the A57 Markham Moor junction.
A spokesman for Nottinghamshire Fire and Rescue said the road will remain closed off for some time and will need to be completely resurfaced before it is allowed to reopen.
The lorry, which was carrying about 20 tonnes of baled straw, was heading north near Markham Moor when the blaze broke out.
Nottinghamshire Fire and Rescue Service sent crews from Retford, Tuxford and Worksop fire stations to tackle the blaze, following the call this morning.
Highways England is advising northbound traffic to follow the diversion by exiting at the Markham Moor Interchange and totake the A638 north on the Great North Road to Retford.
Drivers should then continue along the A638 through the villages of Barnby Moor, Ranskill and Scrooby to the A638/A614 Hawesknest junction, before turning left onto the A614 until Blyth Interchange, then rejoin the northbound A1.
Southbound traffic is advised to exit the A1 at Apleyhead Interchange and take the A614 south and then the A616 east towards South Muskham.
Drivers should then take the B6325 and at the North Muskham Interchange re-join the A1.
Bus operator Stagecoach has also announced its services are being diverted in the area.