"The officer wasn't injured and the patrol vehicle has been towed."
Transmission Gully has been built through a public-private partnership (PPP), the Wellington Gateway Partnership (WGP), with CPB Contractors and HEB Construction subcontracted to carry out the design and construction.
The 27km motorway opened two years later than originally expected.
Police have previously urged people to be careful, despite the excitement over the new road.
"Police want to remind people that this is a motorway and you cannot stop. We appreciate this is a new stretch of road and people will want to look around but we urge drivers to remain focused and drive distraction-free to ensure the safety of all road users."