A spokesperson for National Express said: “We can confirm the National Express 040 service between London and Bristol was involved in an incident.
“Emergency services quickly attended the scene and passengers were safely transferred to an alternative vehicle to continue their journeys.
“We are cooperating with the authorities and will provide any assistance to support their investigation.”
Wiltshire Police have urged anyone with relevant dash cam footage to get in touch.
A separate fatal crash which occurred on Sunday afternoon has also closed the motorway in both directions, between J16 and J17.
An 18-year-old woman was killed after her car left the road.
