Curran was accompanied by fellow Dunedin MP and Health Minister David Clark during a brief appearance to read from a prepared statement outside her electorate office. She left without taking questions.
Ardern said Curran had contacted her last night and they had talked it through.
"There's no doubt there was a huge amount of pressure on her," she told reporters in Gisborne, where she had been announcing a massive Provincial Growth Fund boost for the Tairāwhiti region.
"I think the pressure that she felt was pressure she put on herself."
She admitted Curran had made errors of judgment.
"There is no doubt the minister made a mistake. The pressure she is under is stopping her from doing her job.
"Clare has come to the view the issues currently surrounding her are causing an unacceptable distraction for the Government and immense pressure on her personally.
"I agree with her assessment that resigning is the best course of action for the Government and for her."
Before Curran's resignation became public, Ardern was asked this morning in an interview with Newstalk ZB whether she would fire her. Ardern said she would not.
When asked by reporters about that later, Ardern said: "The question that I was asked this morning was whether I'd asked her to resign, and the answer was no."
Curran took personal leave on Thursday after bungling an answer in Parliament on Wednesday about whether she had used her personal Gmail account for government business.
She was sacked from Cabinet and stripped of her open government and digital services responsibilities by Ardern on August 24 after not disclosing a meeting set up with entrepreneur Derek Handley using her Gmail account.
It was her second strike after failing to disclose a meeting she held with former RNZ head of content Carol Hirschfeld in December last year.
Curran today addressed the use of her Gmail, saying she used it only infrequently for work purposes and it would have been discoverable. She said she had never used it conceal anything.
But National leader Simon Bridges said there were still questions about Curran's use of her private email account.
"Is there information contained in these emails which has forced the resignation of Ms Curran?" he said.
"Jacinda Ardern had two chances to show leadership and sack Ms Curran – when she first misled New Zealanders over secret meetings and then when she did it again recently," he said in a statement.
Curran's portfolios have gone to Consumer Affairs Minister Kris Faafoi, who will become the Minister of Broadcasting, Communications and Digital Media, remaining outside of Cabinet; and Peeni Henare who will become the Associate Minister for ACC.
Curran said she had been proud to be part of the coalition Government.
"During my time as a minister I've worked hard on issues I've really believed in."
She thanked Ardern and her colleagues for their support.
