Brook, who was made white-ball captain last year, will still lead England in the forthcoming T20 World Cup and the limited-overs series in Sri Lanka, beginning in two weeks’ time.
The 26-year-old has performed below his best in the Ashes, scoring 358 runs in 10 innings without a century.
Following the incident in Wellington, England slumped to 31-4 against New Zealand in a match which started at 14:00, including Brook being dismissed for six. The tourists eventually lost by two wickets.
On the same night of the altercation with the bouncer, Brook and England team-mate Jacob Bethell were filmed drinking and the video later posted on social media.
Before the fourth Ashes Test, England director of cricket Rob Key revealed he had spoken to Brook and Bethell about their behaviour in New Zealand, while at the same time confirming he would investigate England’s drinking in Noosa.
“I didn’t feel like that was worthy of formal warnings, but it was probably worthy of informal ones,” said Key.
It has been confirmed Key was referring to a clip of Brook and Bethell on social media, rather then the later incident involving Brook.
England’s off-field conduct has come under heavy scrutiny during this Ashes series.
Coach Brendon McCullum had removed the England players’ midnight curfew, which had been in place since the 2017-18 tour of Australia.
That curfew came into force after England wicketkeeper Jonny Bairstow was accused of headbutting Australia batsman Cameron Bancroft in a Perth bar.
In announcing a review into this winter’s tour, ECB chief executive Richard Gould said “behaviour” will be analysed.
“It doesn’t surprise me,” former England captain Michael Vaughan told BBC Sport.
“For it to have broken on the back of losing 4 -1 in Australia, on the back of what happened in Noosa, on the looseness of the players on the pitch in terms of their discipline with some of their strokes, it kind of tells you that whole culture around the team, the group and the ECB needs to change.”