The admission follows questions by RNZ about what happened at an inner city bar two weekends ago.
In a written statement to RNZ, the mayor said she had a problem with alcohol.
She said that, to her "great embarrassment and shame", her drunkenness seemed to have been recorded.
Whanau said she sought counsel from friends, family and colleagues and has since got professional help.
"I am not a career politician, and leadership positions in public office are not built for regular people who may have struggles with addiction, mental ill health, or any other illness that has stigma attached. We have seen this play out with career-ending moments from politicians across the political spectrum in recent times," her statement read.
"I am a flawed person, but I care deeply about this city. I will continue to represent the hopes and aspirations of my local community and I will do so with the compassion and care of those around me and with the professional help required.
"I would like to say to others struggling with alcohol issues that you can seek help and still commit to your passions, work, family, friends in a way that is meaningful. We are complex, layered people and deserving of love.
"I would appreciate respect and care from the media whilst navigating this period of sobriety and professional support."
Wellington councillor Rebecca Matthews said: “Tory is in a stressful job where there is huge scrutiny, and any of us doing it would have to face whatever demons we had. Her honesty about her own is groundbreaking, and she has had and will continue to have my full personal and political support to keep doing a great job as mayor while addressing the issues she has described.”
In July this year, Whanau was accused of drunken behaviour and failing to pay her bill at a popular Wellington restaurant.
In a statement at the time, the mayor said she “strenuously denies” claims about her behaviour including asking a waiter “do you know who I am?” after being cut off.
Speaking to Newstalk ZB, she admitted she was tipsy while dining at the Old Quarter on Dixon St where she was spotted, but said accusations about her conduct and being refused service were “simply false”.
She told Wellington Mornings’ Nick Mills the failure to pay the bill was a “miscommunication” between friends, and she was “mortified” by the mistake and she apologised to the restaurant.
Whanau said she was “tipsy” and “merry” after a hearty dinner and drinks with a friend, but was in no way drunk. She told Mills she had not been wearing makeup, which may have contributed to why people thought she was drunk.
The Old Quarter general manager Shay Lomas told NZME Whanau was definitely intoxicated, and he confirmed she had asked a waiter if they knew who she was.
”I’d say she was trying to be funny but also not really - it was a mixture of serious and a bit ditzy, there wasn’t anything really disrespectful about it, it was just like “do you recognise me?’”
Where to get help
• If you or someone you know needs support and treatment to reduce their alcohol intake, call the Alcohol Drug Helpline on 0800 787 797, visit their website, or free text 8681 for confidential advice.
- RNZ and NZ Herald