A St John spokeswoman said two people had been taken to Auckland City Hospital with moderate injuries. She could not confirm whether one of them was a child.
Police had earlier said three people had been injured, and all were in a minor condition.
Parts of the road were cordoned off and motorists have been warned to expect delays as traffic management remains in place.
UPDATE 2:50PM Lanes have reopened on Victoria St West in the City Centre following a crash. Continue to expect delays through the area as traffic management remains in place. ^MF https://t.co/tgOXFRNk5L
A second witness, Mark Mallinger, told the Herald he saw a double decker sightseeing bus rolling down Victoria St and a person, presumed to be its driver, running after it.
He heard people screaming after the bus crashed into a construction site on the corner of Victoria and Albert Sts.
Mallinger said he heard a crunching sound as the bus crashed backward through a construction barrier.
He said the bus had gone through an area where pedestrians crossed the road at the traffic lights - and it was busy as it was lunchtime.
Despite the steep hill the bus came to a stop when it hit the construction site.
The bus had started rolling slowly, so he assumed it was being reversed - until it sped up and he saw the driver running after it.
A reporter at the scene said a woman appeared to have been trapped but was freed now.
She was sitting down holding a young child and was being attended to by fire officers. She appeared to have escaped serious injury and was able to walk to an ambulance.