At around 12.30pm, emergency services were called to the southbound carriageway between junctions 35 at Carnforth and 34 at Lancaster.
All three lanes were closed and the van was moved to the hard shoulder.
The fire was reported as being out by 1.30pm and lane three has been reopened.
However, traffic is building and motorists are advised to avoid the area if possible.
It is not known whether anyone has been injured.
Yesterday, one junction further south, a lorry transporting shortbread biscuits caught fire, resulting in lanes being closed for several hours.