The lorry – which was carrying batteries – caught fire between junctions 28 at Alfreton and 29 at Chesterfield at about 2.30pm on Wednesday.
Firefighters battled the blaze as a plume of thick, black smoke spiralled into the sky.
The northbound carriageway will be closed throughout the night as highways workers carry out “extensive repair works” and there is likely to be disruption on the motorway on Thursday morning.
The southbound carriageway was shut but is now open.
A Derbyshire police spokesman advised drivers to avoid that section of the motorway.
Nobody was injured in the incident, the spokesman added.
It is not yet clear how the fire started.
Firefighters and paramedics handed out water to drivers stuck in their cars – as temperatures topped almost 30C.
On Twitter, @RossRobinson_ said: “Not a good time to be stuck on the M1 in this weather.”
@SuzyG70 said: “Stuck on the M1 on the hottest day of the year! Great to see friendly people sharing drinks.”
@LindsayGrahamUK added: “A tad warm this afternoon on the M1 stuck in the tailback.”
Keep checking back for updates.