"It's probably just going to be very heavy for the rest of the afternoon and for the drive home."
Rubberneckers are also making the delays worse, the spokeswoman said, including on the northbound lanes heading towards the city.
The worst congestion was through the Ellerslie, Panmure area.
"There's quite a bit of grit on the road and obviously there is still part of a broken truck sitting off to the side and there's a big broken VMS sign - so there's quite a lot to interest people as they drive through.
"So they are slowing down to have a look. There is a lot of rubber necking, so that is really slowing things down."
The agency recommended traffic heading south from the North Shore to consider using a longer route around State Highways 18, 16 and 20.
The NZTA spokeswoman said the incident happened when the trailer unit of the rubbish truck started to lift.
"As it was driving along the motorway it started to lift up and that is why it hit into the bridge. So it wasn't just someone driving along and blindly ignoring the fact that they had a load that was too big."
Meanwhile, all southbound lanes on State Highway 1 at Ellerslie will be closed tonight for emergency work.
The southbound lanes will be closed from midnight until 6am tomorrow, from the Ellerslie Panmure southbound off-ramp to the Mt Wellington southbound on-ramp.
Motorists are being advised by NZTA to use the alternative Great South Rd route.
Police Northern Communications Shift Inspector Chris Tate said earlier today that the truck had struck the bridge that spanned the motorway.
"It's hit the bridge and its load is all over the road," Mr Tate said.
He said the clean-up operation would take some time.
Mr Tate said traffic was not only blocked on the motorway but beginning to clog streets connected to on-ramps.
Its driver was not injured, he said.
Electrician Greg Wilcox said the moment the rubbish truck hit the bridge sounded like an enormous explosion.
Mr Wilcox said he was just 50m away when the accident happened.
"I was just outside by my van when I heard this almighty bang like a bomb going off - it was huge - enough so people starting coming out on to the street.
"As it happened I turned toward the bridge and I saw the truck as it went by.
"It had obviously lost all the big dump tray that sits on the back."
The driver was sitting in his cab 200m further up the road.
Mr Wilcox said it was likely there were a number of near misses of cars swerving to avoid the wrecked truck and its spilled load.
NZTA is encouraging motorists to make use of travel information services, which it says will help commuters decide on the best time to travel and how to stagger their journey to avoid the most congested periods, as well as offering information about alternative travel routes.
The agency is also advising motorists to explore other transport options including buses, trains, walking and cycling.
"[But] if you are stuck in traffic be patient and courteous, everyone else is in the same boat as you. Try to stay in your lane, merge carefully so that you're not blocking other traffic behind you, and be courteous to other drivers around you by letting them change lanes.
"As tempting as it is to slow down to look at an incident on the motorway try and avoid that, even very small changes in speed can have an impact on cars kilometres further back in a queue."
