Seven people were in the car, and two others had moderate injuries.
The spokesman said the weather has been "extremely inclement", and power outages meant no lights were on along the motorway.
He said the tree "came straight down on top of the car".
A member of the public following the vehicle pulled all seven occupants out after the crash. The passengers were aged from 5 months old to their early 50s.
The road remains closed to south-bound traffic from the Papakura off-ramp, and the serious crash unit is at the scene. Police said the road would remain closed for at least an hour.
Meanwhile, homes in Otahuhu, Mt Wellington, Otara, Mt Albert, Glen Eden, Titirangi, Oratia and others are without power, according to Vector.
The total number of households affected is 4696 according to Vector, and 2692 of those are in Otahuhu/Mt Wellington.
There are also reports of power outages at Pokeno and Tuakau.
A Vector spokeswoman said they were hoping to get power restored before 1am.
"The weather's played havoc with our network. We're doing our best to get the power back on."
She said they would "hopefully get it back on before then, but it depends on the weather".
She said strong winds had brought down power lines, and caused trees to fall on them.
In Otara and Otahuhu, the cause is given as an emergency shutdown for repairs, in Mt Albert the power was shutdown for emergency reasons.
Lines down have caused outages to 322 households in Glen Eden, while feeder faults cut electricity to 780 homes in Tititrangi and 842 in Oratia.
Strong winds and rain are forecast for much of the North Island, and western parts of the South Island, tonight and into Sunday morning.
People took safety indoors while the wild weather wreaked havoc around them, including Lorde's mum Sonja Yelich who took to Twitter.
