A Bedfordshire Police spokesperson confirmed that an air ambulance has been called.
The statement said: "We are currently at the scene of a serious collision on the M1. Emergency services were called shortly after 1.30pm today (Sunday) following reports of a collision between junctions 13 and 14 on the southbound carriageway.
"A full closure of the southbound carriageway is currently in place. The northbound carriageway is temporarily closed to allow the air ambulance to attend the scene.
"We would like to thank everyone affected by the closures for their patience, and we ask anyone planning to use the M1 to seek alternative routes at this time."