Cheshire Fire and Rescue Service said firefighters used specialist equipment to lower themselves down to reach the driver.
Crews used water to cool the lorry.
Bunding was used to contain a leak of about 1,000 litres of bio-diesel from the vehicle’s fuel tanks.
Police urged motorists to avoid the area following the incident.
National Highways said: “A complex repair operation is under way and will continue throughout [Tuesday] morning.”
