Indonesian media have named her as Myra Williams from Taupo.
Williams reportedly flew to Denpasar from Melbourne and was questioned by Indonesian authorities over allegations she brought the drug into the country with her.
A Bali airport policeman told NZME Williams had appeared confused while lining up for her passport.
"Complaining, something like that. The immigration think she is drunk," he said.
The policeman, who spoke little English, said she took a rest on the sofa for about 30 minutes.
"I think she is drug, like 'ice' ... have small plastic on her."
The policeman said they'd found it on the sofa next to her where she was taking a rest.
"Then the narcotic department bring her to Denpasar ... department of narcotic."
He confirmed immigrations, customs and the narcotic department had all spoken with the woman.
The policeman believed Williams had been detained by the Denpasar narcotic department - but had no further information.
Williams, who lives just south of Melbourne, posted on her Facebook that she was "so damn excited" to be going to Bali.
Indonesian news outlet RadarBali.com reported a 27-year-old woman, who was born in Hamilton, had landed at Denpasar, from Melbourne, on Air Asia flight 801.
MFAT says the New Zealand Embassy, Jakarta, is in contact with the local authorities and providing consular assistance.
It confirmed a New Zealander had been arrested - but was unable to confirm their identity.
The Ministry is providing family with updates and consular advice.
A spokesman says it cannot comment on or interfere in the judicial proceedings of another country, as is the case with all arrests and detentions involving New Zealand citizens overseas.
