Several incoming flights were also diverted away from the airport earlier today, and there were delays for those trying to leave.
Air New Zealand had warned customers further disruption is expected today, and travellers should consider delaying any non-urgent travel.
Air New Zealand customers who don't urgently need to fly will have the option to transfer their booking to another date, or hold the fare value in credit for up to 12 months.
The halt on activity at Wellington Airport was the latest in a string of weather-related travel dramas.
Flights were grounded at Auckland Airport yesterday, where winds of 90km/h were recorded and gusts reached up to 120km/h.
Auckland Transport is advising people to only travel if essential.
NZTA says 127 traffic lights were out across the city today, including the signal lights on motorway on-ramps.
Several roads were closed, and there were delays on some rail lines.
Around 180,000 Auckland homes were initially without power as a result of the storm last night.
Now, 90,000 houses are still without power, with an estimated repair time of two to three days by Vector.
Winds gusts peaked at 213km/h at Manukau Heads last night. Auckland city was battered by winds averaging 120km/h.
Fire and Emergency New Zealand received 1200 calls as a result of the storm.
There is a moderate risk of thunderstorms in Auckland, Northland, Waikato and Waitomo on Thursday and Friday.
A strong wind watch is in place for Auckland from Thursday night to Friday morning.
