"There's a bit of damage to the house," he said.
Police are asking motorists to avoid John St.
A spokesperson said the bus driver suffered minor injuries in the crash and was taken to Wellington Hospital in an ambulance.
There were no passengers on the bus at the time.
No members of the public or bystanders have been injured.
The northbound lane of John St near the Countdown is closed and traffic is building up in the area.
Wellington man Gundeep Singh said he was driving past when he saw the scene of the accident.
"There was damage on the corner of the house because the bus literally hit the wall of the house."
Singh said there were people gathered around and a long line of traffic because one of the lanes was blocked.
The road is expected to remain closed for some time while heavy lifting equipment removes the bus.
