The Daily Telegraph report said the incident occurred on October 31, the night before England's third one-day international against the hosts.
England went on to lose the match, ensuring a 3-0 series sweep for New Zealand, with white-ball captain and batsman Brook scoring just six runs in the ODI in Wellington.
The news is the latest setback for England's board (ECB), which is dealing with the fallout from a 4-1 Ashes series defeat in Australia and looking into reports that players drank excessively during a break between tests in Noosa.
"I want to apologise for my actions," said Brook, who was the third-highest scorer during the Ashes series with 358 runs, in statement to British media.
"I fully accept that my behaviour was wrong and brought embarrassment to both myself and the England team.
"I am determined to learn from this mistake and to rebuild trust through my future actions, both on and off the field. I apologise unreservedly and will work hard to ensure this does not happen again."
The ECB said it was aware of the incident and that it had been dealt with through a formal and confidential disciplinary process.
"The player involved has apologised and acknowledged their conduct fell below expectations on this occasion," it added in a statement.
ECB chief executive Richard Gould said the governing body had already begun a "thorough review" of the Ashes campaign, which ended yesterday with defeat in the fifth test in Sydney.
"This will cover tour planning and preparation, individual performance and behaviours, and our ability to adapt and respond effectively as circumstances require."
