The $85,000 public art installation was damaged on January 11 or 12, while the garden was closed.
Community Constable Louise France, of North Dunedin, said police were still investigating the incident.
Dunedin Botanic Garden team leader Alan Matchett said yesterday the estimated cost of fixing the damage was $700-$800.
Anyone with information about the incident is asked to contact Const France on 473 0737.