An air ambulance was understood to have air-lifted a casualty from the scene between junctions 20 and 21 in the Kirkpatrick Fleming area.
A Police Scotland spokesman said diversions had been set up and the route was likely to remain closed to southbound traffic for some time.
He said the first reports had come in around 4 pm.
An accident investigation was underway but no details of any casualties was yet available.
Drivers in the area stated one extensively damaged vehicle involved ended up on an embankment and other vehicles were stationary nearby.
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