A New Zealand Transport Agency spokesman said traffic in the area was still "heavy".
"Soon they will be bringing a crane in to remove the truck, so there is going to be quite a lot of disruption in and around both southbound and northbound lanes.
"We are trying to work hard to get it open by evening peak, but there is a risk that we might have a reduced lane for northbound during the evening peak.
"There is going to be delays in that area right throughout the day."
He said the Transport Agency was encouraging motorists to use public transport, or take an alternative route.
Motorists travelling southbound from the Kapiti Coast were advised to use SH58 and SH2, he said.
Those travelling from the Churton Park and Johnsonville area could take diversions through Ngaio, he said.
Diversions were also in place through Johnsonville and down Moorefield Rd.
"They are heavy as well so [drivers] certainly will need to allow extra time if they are travelling at any time today."
The driver of the truck was treated at the scene by staff, and the police commercial vehicle investigation unit was investigating the cause of the crash.