The claims were recorded as having "Pokemon" as part of the accident description.
The majority of claims, 11, were for injuries that fell into the soft tissue injury category, such as bruises and strains. The single largest claim paid out by ACC last year was $779.
The injury claims follow overseas reports of people hurting themselves while playing the game.
From fractured bones, bruises, blisters and sunburn, there were also reports of serious slips and near-accidents on roads.
In the UK last month, a 24-year-old was seriously injured when she slipped and fell in woods near Chesterfield, South York, while playing the app.
She suffered injuries to her back and neck and had mild hypothermia when paramedics got to her.
A 14-year-old boy was also seriously hurt when he was hit by a car near Spalding, Lincolnshire.
There were also reports of thieves using the app to their advantage - by using a feature of the game called a lure, which attracts Pokemon characters to a particular area for a set amount of time.
Thieves targeted players by luring them to a spot before attacking them stealing their possessions.