The girl was admitted to Kaitaia Hospital for the treatment of a suspected broken arm and minor bruising on her head and face. Mr Beatson said police were concerned about the random nature of the attack and the level of violence involved.
"This could have been anyone's daughter walking through town minding their own business," he said.
"The theft and attack were totally unprovoked, and we are treating it seriously.
"We want to find the people responsible."
The investigation was well under way, but Mr Beatson was asking witnesses to come forward.
"We understand that some passersby stopped to see if the victim was okay during or immediately following the incident.
"But because she was upset and disoriented they were unable to help her. We want to speak to these people, and any other witnesses who saw the incident unfold."
Any information should be passed to the Kaitaia police on (09) 408 6500 or anonymously to Crimestoppers on 0800 555-111.
Mr Beatson said the cap was unlikely to have been discarded.
"Like magpies, this couple will probably have kept it because it was shiny and brand new," he said.
"A friend, family member or neighbour has most likely seen them with the cap, and we want to hear from those people too."