The proposals for the project in a neighbourhood west of the city's downtown area gained 206 votes in favour, compared to 24 votes against.
It is understood dozens of makeshift mosques are catering to the thousands of Muslims living in the city, some of whom have arrived in the migration crisis.
The Greek Education Minister Nikos Filis has reportedly suggested the new taxpayer-backed mosque could help prevent followers of Islam being radicalised.
He was quoted by the Athens-based newspaper, Kathimerini, as saying: "If we wish to avoid the problems facing France and Belgium, we should not make the mistakes that they are now trying to deal with.
"The existence of makeshift mosques is a shame for the country as well as for the Muslim community and a danger to national security."
In addition to meeting opposition from the Greek Orthodox Church, the proposed mosque was also resisted by the right-wing Independent Greeks (ANEL) and far-right party Golden Dawn.
Premier has approached the Church of Greece for a comment.