The southbound carriageway at Junction 4, Bromsgrove, has been closed so the lorry can be recovered and damage to a bridge over the motorway can be assessed.
Emergency services are at the scene but Highways England warned drivers to expect long delays while the incident is dealt with.
Drivers heading southwards on the motorway - which starts in the Black Country, passing through West Bromwich, Oldbury and Halesowen - are being ask to allow extra time for travel.
It means major disruption for travellers heading southwards to places like Devon and Cornwall for weekend breaks.
Highways England has reported congestion spanning 5.5 miles and "long delays of at least 60 minutes above usual journey times approaching J4".
The Government agency tweeted: "Road users are advised to allow extra time for their journeys."