The road is expected to remain closed for several hours while lorry is recovered.
Thousands of motorists in the South West have been warned about the dangers of driving through red X road closure signs on motorways.
Traffic was brought to a standstill after the lorry, which was carrying hay, caught fire on Wednesday (March 13) evening.
The tunnel is one of several ideas being considered to upgrade the road.
Highways England wants local people to have their say on plans to upgrade the A417 near Birdlip in Gloucestershire.
Highways England has launched a consultation on proposals to improve the single carriageway section between Sparkford and Ilchester.
Highways England says the M5 northbound between junctions 16 and 14 has been fully reopened following the serious incident in South Gloucestershire on Saturday.
One lane had remained closed between junction 15 and junction 14 while police investigations continued.
The carriageway reopened fully at 5pm.
Highways England says drivers should be aware of residual delays in the area.
Heavy traffic on the M5 following a lorry breaking down and spilling diesel earlier today. Drivers advised to allow extra time for journeys.