Sherin Khankan, born in Denmark to a Syrian father and a Finnish mother, said that while all activities at the Mariam Mosque except Friday prayers would be open to both men and women, all imams would be female.
"We have normalised patriarchal structures in our religious institutions. Not just in Islam, but also within Judaism and Christianity and other religions. And we would like to challenge that," she told AFP.
Reactions from the city's Muslim community had mostly been positive, with negative feedback being "moderate," she said.
Khankan, a well-known commentator and author in Denmark, said there was "an Islamic tradition allowing women to be imams" and that most of the criticism was based on ignorance.
Similar projects by Muslim women exist in several other countries, including the US, Canada and Germany.
Imam Waseem Hussein, the chairman of one of Copenhagen's biggest mosques, questioned whether there was a need for the project.
"Should we also make a mosque only for men? Then there would certainly be an outcry among the Danish population," he told daily Politiken.
Khankan said that original reports that the location of the mosque was to be kept secret due to security concerns were incorrect.
"We haven't received any threats whatsoever," Khankan said, adding that she wanted to collaborate "with everyone" within the Muslim community, and that the project was not about judging or excluding anybody.
The first Friday prayer has yet to be held as another eight female imams, in addition to the two currently involved, have to be found.
"It's a big responsibility and we all work as volunteers," she said.
The longstanding political influence of the anti-immigrant Danish People's Party, as well as the row over Prophet Mohammed cartoons that led to deadly protests in Muslim countries, have strained relations between Denmark's largest religious minority and the majority population.
Denmark's largest purpose-built mosque, including the country's first minaret, opened in 2014 in a gritty district in northwestern Copenhagen after receiving a 150 million kroner (€20.1 million, $22.6 million) endowment from Qatar.