The accident is reported to have happened close to Redworth Road junction at Shildon.
Traffic is being diverted to the A68.
The road closure is affecting bus services.
Arriva North East tweeted: “Services 1/X1 Darlington to Bishop Auckland.
“These services will divert via the A68. We are currently unable to serve Heighington on the 1 or Shildon on the X1.”
A spokesperson for Durham police said: “The A6072 – Redworth Road between Heighington and Redworth is currently closed in both directions due to a road traffic accident, and may be closed for some time whilst investigations continue.
“An update will follow in due course.”