It comes on top of $18m the previous National Government committed for the rebuild of the Auckland City Mission, which is now expected to cost $85m.
Mission CEO Chris Farrelly said the organisation had opened an addiction centre in 1982 on a temporary, ad-hoc basis, but it was still being used today.
It was initially for treating alcoholics, but today the problem was mostly methamphetamine and, increasingly, synthetic cannabis - "an evil concoction", he said.
The new funding would cover the costs of two floors of the new development, and increase the number of detox beds in Auckland from 20 to 30.
"A huge number of Kiwi families will have experienced the terrible harm and distress that come from alcohol or drug dependency," Ardern said.
"As a community we need to do more to support people living with addiction."
She said dedicated detoxification and treatment programmes made a significant difference.
"Demand for these services is high and too often people are waiting too long to get the help they need."
Health Minister David Clark said the city mission's detoxification services were "tried and true".
"They have outstanding GPs, nurse practitioners and social workers with specialist qualifications in alcohol and drug counselling, mental health, Te Ao Māori, elder care and violence and trauma."