Six fire crews, South East Coast Ambulance Service (Secamb) and officers from Surrey Police attended the scene.
National Highways said a separate incident closing the east tunnel at Dartford meant the M26 diversion route was “severely congested”.
A spokeswoman for Surrey Fire and Rescue Service said shortly after 07:00 BST on Monday that there was still one engine at the scene.
She said: “The crew are currently dampening down hot spots.
“We’d like to take this opportunity to thank all staff and partners who were involved in tackling this blaze.”
Surrey Police said: “The M25 remains affected in both directions between J5 and J6.
“The anti-clockwise carriageway has reopened, but lane 3 and 4 (of 4) remain closed within J6.”
National Highways added that specialist recovery would be required and the road surface would likely need to be resurfaced.
A Secamb spokesman said: “Secamb were called at 22:20 last night to reports of a fire on the M25 between Clacket Lane and Junction 6 involving a lorry.
“Crews assessed one patient with minor injuries, who was discharged at the scene.”