She placed third in the seat, but entered Parliament through the list.
Green Party co-leader Chlöe Swarbrick said she was made aware of the issue on Tuesday.
She said while the payment was declared to the Electoral Commission, the failure to carry an authorisation statement was serious.
“The Greens take really seriously compliance with electoral law. To that effect, we’ve had conversations with the Green Party itself, and my understanding is the party has referred it on to the Electoral Commission,” she said.
Swarbrick said the process now sat with the Electoral Commission.
“The law says that this sits with candidates, and the Green Party make it abundantly clear to all of our candidates across the country that this responsibility sits with them.”
The Electoral Commission confirmed it had been contacted by the Green Party, and said it would look into the issue and make inquiries with Tana and Verve Magazine.
Failing to include an authorisation statement in an election advertisement could lead to a fine of up to $40,000, according to the Electoral Act.
Tana remains absent from Parliament.
She was stood down on March 14, after Stuff reported allegations of migrant exploitation relating to her husband’s e-bike company.
An investigation into the MP has now lasted nine weeks, and cost $43,000 so far out of the Green Party leaders’ office budget.
Swarbrick said there was no further update on that investigation.
“It’ll be done as soon as it is done, and I guarantee you I am looking forward to giving you an update when that has happened.”