The movie, They are Us, will focus on the prime minister's response in the week following the attacks, and is set to star Australian actress Rose Byrne as Jacinda Ardern.
Ardern said in a statement that plenty of stories from 15 March could be told, and she does not consider hers to be one of them.
New Zealand's Muslim community has come out against the film, saying the focus on the prime minister, rather than the victims, is wrong, and it is just Hollywood profiting off the community's pain.
More than 58,000 people have so far signed a petition to shut the production down.
In a statement, producer Philippa Campbell said she deeply regrets the shock and hurt the announcement of the film has led to throughout Aotearoa New Zealand.
Campbell said she listened to the concerns raised over recent days and heard the strength of people's views.
She now agrees that the events of 15 March, 2019 are too raw for film at this time and does not wish to be involved with a project that is causing such distress.
She said the film did not take enough account of the political and human context of the story.