A police media adviser said police were called to Earnslaw Park, in Beach St, about 3pm in response to the incident.
"Two people were reported to have minor injuries from the incident."
An arborist had been contacted to clear the tree.
Strong wind and heavy rain watches have been issued for today as one of many fronts moves over the South Island.
Strong northwest winds may approach severe gale speeds in exposed parts of the Queenstown Lakes and Central Otago areas between 8am and 4pm and northerly winds may approach severe gale force in Fiordland between 6am and noon today.