The branch from the American white ash near McDonald’s in George St came down about 3.15pm on Wednesday, landing on the back of a vehicle.
Dunedin City Council parks and recreation acting general manager Scott MacLean said a branch above seats was to be removed yesterday and the rest of the tree could be removed next week.
Mr MacLean said a nearby plane tree was in poor health and it would be removed as well.
The rest of the American white ash tree was a risk to pedestrians and motorists, he said.
"We inspected the tree and it is likely it was affected by the high winds last weekend. The branch may have broken at the weekend, but it can take a day or two for it to detach."
The tree had a blackened section where the branch had detached.
This was probably caused by a build-up of diesel soot and fine soil from the city air.
George St trees are inspected annually.
