It is understood that the person was on the footpath on King Edward St, near the Oxford St intersection, when the incident occurred, about 4.35pm on Wednesday.
The southbound ute knocked down a couple of posts on the incorrect side of the road and mounted the footpath before spinning backwards across the street and coming to rest, partly on the footpath on the correct side of the street, at some stage hitting the wheelchair.
A woman whose vehicle was nearly hit by the ute said she thought the ute's driver may have had a medical event, but police have not confirmed this.
The driver of the ute also remains in Dunedin Hospital, in a moderate condition.