Emergency services are currently at the scene on the Northbound carriageway of the J23 exit at Loughborough. Traffic on the M1 Northbound approaching the J23 exit has been released.
The slip road remains closed while fire crews continue to damp down the lorry, LeicestershireLive reports.
Highways England says it is expected to be some time before it re-opens due to the heavy load.
Leicestershire Fire and Rescue crews have been tackling the blaze.
Traffic had been building on the M1 Northbound while it was temporarily held.