Ms Stewart said she had collected her luggage when she was stopped by Customs officers. She was questioned about her ticket - which had been bought by Mitchell - and told the purchase by another person and her passport being only recently granted had raised "red flags".
Ms Stewart said she gave Customs staff the phone numbers for Mitchell, who was due to arrive in a few hours, and for the New Zealand person who was collecting her from the airport.
She said shortly after she heard the officers referring to "Kim Dotcom, mega billionaire". She said she believed Mitchell's number allowed officers to connect her to Dotcom.
Ms Stewart said she had not mentioned Dotcom. "I was unsure of his status. I didn't know if I should or shouldn't. I was here because I was invited for my birthday."
During the questioning, Ms Stewart was made to show her bank account balances and to submit to a strip search.
"I've never in my life been through anything like that before. I was in tears."
She said she asked for a lawyer and was told she would have to submit to further detention while one was found.
She was released after the woman collecting her at the airport started ringing around to find out where she was. Before being released, Ms Stewart's visitor visa was cut from three months to two weeks.
Just hours after she was let in, Mitchell landed and was also detained. He said he was questioned for three hours about whether he was working in New Zealand.
Mitchell said he and Printz Board, a music producer, had both given their time to co-produce the Flight of the Conchords song for the Cure Kids telethon. Mitchell said: "I wasn't paid for it - it's raising money for sick children."
It is not the first time visitors with a connection to Dotcom have been detained and searched at Auckland Airport. Hollywood documentary maker Donovan Leitch was detained and questioned when he visited in March to discuss making a film about the Dotcom case.
A police spokesman said there was no active investigation into Dotcom.
A spokeswoman for Customs said Ms Stewart was not detained because of any connection with Dotcom. She did not respond to questions about whether associations with Dotcom raised any alerts with Customs.
