Darby emailed his concerns to council chief executive Stephen Town, saying his greatest concern is the investment in British American Tobacco.
"To find out council is invested in a controversial tobacco company in the week we are about to review the Smoke Free Policy is a complete embarrassment," he said.
Auckland Council Treasurer John Bishop said the council had confidentiality restrictions with some of its fund managers which prevented it from disclosing specific asset holdings.
American-based Janus is one of 11 fund managers managing a $320 million diversified asset portfolio of shares, bonds and other assets held by council.
The portfolio originates from funds held by legacy councils. Investments are made through a range of fund managers, based in New Zealand and overseas, and advice is taken from a professional investment adviser, Bishop said.
"As part of this process we continually look to align our investment policies with best practice, including those associated with responsible investment. Auckland Council has a responsible investment policy which is regularly reviewed in association with our overall investment policies," he said.
In a written statement, Town said the diversified asset portfolio is being sold down over the next two to three years, which is consistent with last week's announcement on removing sugary drinks from leisure centres.
Councillor Cathy Casey responded to the story on social media, saying it was embarrassing.
Action and Smoking on Health (ASH) and Hapai Te Hauora (Hapai) as the National Tobacco Control Advocacy were disappointed at the report that Auckland Council has investments in soft drink, alcohol and tobacco companies and called for councillors to rectify the situation.
"Being a supporter of Coke and tobacco through investments, as well as trying to protect our communities from the same products is confusing for communities. Time to show Auckland and the rest of the country that change from the inside is going to happen and that creating healthy spaces for communities isn't just for show," said Zoe Hawke Manager, of Hapai Tobacco Control.
Dunedin City Council lost $380,000 this year when it sold shares in four equities - BHP, Origin, Rio Tinto and Woodside Petroleum - which went against its ethical investment policy.
The shares were bought for $1.568 million and sold for $1.187m.