Mr Symonds said the incident occurred in international waters but New Zealand police had jurisdiction when an offence carried a maximum penalty of two or more years' jail.
Tasmanian and Australian federal police had been informed. The arrest showed the police were determined to act against domestic violence.
"You're not going to get away with it, no matter where it happens," he said.
Christmas traditionally sees an increase in domestic violence in Northland, attributed to greater consumption of alcohol and increased financial pressures.
The ship visiting the Bay of Islands that day was the 4000-passenger Voyager of the Seas. On the same day, a 74-year-old passenger was issued with a formal warning after police said she tried to steal jewellery from a Paihia shop. The jewellery was returned and she was allowed back on to the vessel.