There are no reports of injuries.
But police said "motorists are advised to avoid the area due to significant congestion".
NZTA added: "The right lane will remain BLOCKED for some time this afternoon to allow for a complex vehicle recovery.
"Expect up to 15-minute delays in both directions on #SH20. Consider delaying your journey or using an alternative route."
Elsewhere on the Southern Motorway, a breakdown is blocking the right southbound lane on after East Tamaki Rd off-ramp.
NZTA says motorists should "expect delays" in the area.
Traffic would be "heavy" in the area.
And further south at Takanini, a breakdown initially led to the closure of one southbound lane.
While that has now been cleared, NZTA says the incident would lead to delays of around 35 minutes.