Gwent Police was called to the incident near Raglan Services at about 11:30 BST on Sunday.
The ambulance service said a patient had been taken to Bristol Royal Infirmary.
The road was closed in both directions between Monmouth and Raglan for about four hours but police said traffic was now moving freely.
A person has been taken to hospital by air ambulance following a serious crash on a major road in Monmouthshire.