The time limit in the airport's free drop-off zone was about improving traffic flow and safety around the terminal.
Anyone wanting a longer farewell would have to find a spot in the carpark.
Dunedin Airport chief executive Dan De Bono spoke to RNZ's Checkpoint programme earlier this month and confessed he was "a hugger".
They were trying to have a bit of fun with the announcement, he said.
"It's caused quite a stir, we've got quite a bit of conversation going."
CNN included it in it's weekly travel newsletter under the headline "Catch flights, not feelings".
The New York Post went with the "inhumane" angle, while the Times of India said the "quirky rule" had "sparked lively debate online".
The UK's Independent site took things to a more serious level, noting that in the UK more than a third of major airports had raised drop-off fees for drivers in the past year.
"Seven out of 20 airports analysed have raised so-called 'kiss and fly' charges - which are typically levied for dropping off someone as close to a terminal as possible."
A Facebook post with a photo of the "Max hug time 3 minutes" sign has also had more than 56,000 likes and more than 1400 comments.
"You can't put a time limit on hugs! That's inhumane," one person wrote.
Others were more supportive, suggesting other places such a limit would help.
"OMG school drop off lines need a similar sign (Max hug time 10 sec)."
The story has gained the attention of international news media.
