Traffic was diverted around the fire between junctions between junctions 36 for Kirkby and 39 for for the A6.
Police say the motorway was closed after smoke billowed across the carriageways.
The southbound carriageway re-opened at around 10.30am.
One lane on the northbound carriageway re-opened at around 11.30am however police advised this may close again as recovery and clean up continue.
Northbound traffic has been advised to exit at J36 and divert via Kendal using A590 and A6 to rejoin at J39.