The tree, a much-photographed attraction at Roys Bay, was discovered damaged early yesterday - several branches had been removed and discarded on the shore.
Police said today they wanted to hear from anyone who saw or heard anything suspicious in the area overnight on Tuesday.
Meanwhile, tourists, visitors and locals have been asking why someone would attack the tree.
When Paul Hanninen, of Finland, arrived at the lakefront at 4am yesterday to take a sunrise photograph of the tree, he said he thought there was something different about it.
The tree became a popular tourist destination after Lake Wanaka Tourism promoted it on its website in 2014.
On hearing branches had been cut from the tree, general manager James Helmore said he ‘‘deplored this senseless act of vandalism and I would encourage anyone who might know anything to come forward to identify the person or people responsible for doing this.’’
Although the tree was used extensively in marketing it was not the only reason visitors came to Wanaka, he said.
Land Information New Zealand group manager land and property Stephanie Forrest said the tree was actually on Linz land, as the agency was responsible for administering the lakebed.
She said the agency was disappointed to learn of the attack on the Wanaka tree.
‘‘We know how popular this tree is with both locals and visitors alike and is famous on Instagram.’’
Linz had had requests and issued recreation permits for commercial filming and photography of the tree, most recently a reality show.
These often included strict conditions to ensure the tree was protected, she said.
The agency had reported the incident to the police and encouraged anyone with any information about the matter to contact Wanaka police, Ms Forrest said.
Queenstown Lakes District Council spokesman Jack Barlow said although the council was not responsible for the Wanaka tree, ‘‘we are saddened to see any tree vandalised and strongly condemn this type of behaviour’’.