The lorry jack-knifed on the southbound carriageway, near Haggs, at 0430 BST, leaving the 45-year-old driver with serious back injuries.
The road, which serves as a main route to Glasgow, Stirling, Perth and Dundee, was reopened by police at 1245 BST.
The birds were being transported by Noble Foods from a farm in Perthshire to an abattoir at Gainsborough in Lincolnshire when the crash happened.
It took police and specialist chicken handlers from Noble Foods nearly nine hours to clear the scene as hundreds of the birds ran free in the accident area.
Ch Insp Donald McMillan said: “Around 400 chicken carcasses have been cleared from the scene and the road has now reopened.