Contractors are using a digger to clear debris from the area.
But weather conditions in Wellington were stunning today, with sunshine forecast throughout the whole day and a high of 16C.
MetService marine forecaster Mike O'Connor said the swells would have been a result of a deep low passing over the south and east of the country today and strong southwesterly winds over the country.
"We've had quite a strong southwesterly over much of the country today - but Wellington was in a nice little pocket, where we were getting sheltered from the South Island.
"So that low has moved east and it's kicked up this big swell that's come from the southern ocean.''
Tomorrow's weather forecast shows a showery morning with sunny spells and a high of 12C. There is also due to be a southerly change - which will again see big swells.
"The swell is still going to be big tomorrow. What we've got right now is probably slightly higher than what's going to be tomorrow - but it's still going to be pretty large tomorrow.
"We're expecting the swell to ease up tomorrow, but then it picks up again [later in the day]."
Mr O'Connor said swells could reach heights of between 4 to 6m, especially around more open areas including Cape Palliser.
Roads closed
Wellington City Council said the eastern end of Lyall Bay- Moa Point Road was closed due to "high seas", and that drivers should take care if driving south coast roads.
A Wellington City Council spokesman said road closures started from the eastern side of Lyall Bay, near the airport, and included Moa Point Road - where debris had blocked off parts of the road.
Crews were currently working to clear rocks and debris from the area and it was not yet known when the roads would be reopened.
Spokesman Clayton Anderson said: "They'll be making a call sometime tonight. But if you're driving to the airport tonight, then take the main route. Don't take the southern coast route because you won't get through.''
Mr Anderson said the high tide had come in around 3pm and conditions looked to be dying down now (just before 5pm).
The council and emergency services were, however, continuing to ask members of the public to stay away from the area as conditions remained quite dangerous.
"There have been a lot of people coming out to watch, so we're just asking people to stay away. The waves are unpredictable.''
He said people could keep updated about the situation and road closures via the Wellington City Council's social media pages on Facebook and Twitter.
A police central communications spokesman said two people had been trapped in a vehicle on Cape Palliser Road after waves damaged part of the road.
But they had since escaped and both were okay and did not need assistance.
Police said they had also been called out to the same area after reports of cars in danger of being swept out to sea.
"But the owners have organised [tow trucks] to come out, so that's okay too now.''
The Fire Service said they were keeping an eye on the situation but had so far not received any calls from the public.
Julia Price, of Miramar, was driving along Lyall Parade when she decided to stop in a carpark near the edge and have a closer look.
"I was just sitting in my car after I pulled in there, just watching the waves. But then I could see a swell that looked much bigger and thought: 'Ooh, I better reverse my car'.''
She was right. Seconds after pulling out of the carpark, a huge wave crashed over the top of the edge and onto the road - where she had been parked second before.
"It just came straight over. It was incredible.''
Miss Price - who has since gone to higher ground - said there were lots of people out and about watching the action.
She said the weather conditions were fine - no wind and with a perfect blue sky - so could not understand what was causing the dramatic waves on the water.
"There are really, really high tides as well, so I don't know what's happening. But it's a beautiful day here. It's so calm - it's just the huge swells. And I think that's why lots of people are coming out to watch.''
Doug Weir has lived on Lyall Parade for almost 30 years. He said the waves were as big as he had ever seen them.
"We've probably had this four or five times in 25-30 years...it's not a stormy surf, it's just clean cut [and] dead calm. She's one of the bigger ones that's for sure."
The waves were coming over the road, Mr Weir said, and were throwing debris onto the west side of the parade by the Maranui Surf Club, as well as down by the airport.
"It's as big as I've seen here, it's monstering the breakwater out there, running right over it."
He said the waves had drawn a "hardy crew" of surfers, who were making the most of the conditions.
The big waves mesmerised Ingrid Cuttiford, who observed the scene from a restaurant balcony between Owhiro Bay and Island Bay.
She said waves perhaps 15ft (4.5m) high engulfed the pyramid-shaped rocks in the area.
"Rubble and rubbish and debris" were churned up all along the waterfront, she said.
"It's actually been quite a spectacle to watch.
"The slipstream that occurs when the wave blows back on itself has been causing rainbow effects all over the foreshore.
"I'm mesmerised by the beach when it's like that."
She said the waves were undercutting the pathway in places.
"A little bit more of that and it could easily take it right away. At Island Bay, the actual beach wall has been breached."