The government edict came to light last week when a team of girls from Tonga High School were pulled from a touch rugby tournament because of their gender.
A letter from the Pacific nation's education department said the ban was to "preserve the dignity of Tongan women and hold on to Tongan cultural values", according to a translation published by the Matangi Tonga news website.
Adams, who was born in New Zealand but is fiercely proud of her Tongan heritage, described the move as "misguided and stubborn misinterpretation of the Pacific island nation's culture”.
"According to this way of thinking, a proud Tongan like myself, could not attain the standing I have in this world," she posted on Facebook. "Tongan women must be free to choose their destiny, and not be held back."
Adams has won two gold and one silver in Olympics shot put and is favourite to claim a fourth Commonwealth Games gold on the Gold Coast next month.
"Rugby, like any sport, ought to be embraced by our Tongan women — we're good at it — don't take it away!" she said.
Ardern said she disagreed with the ban but would not use New Zealand's aid programme as leverage to try to have it overturned.
"As a school student I played touch rugby and I would encourage all the young women to engage in whatever sporting code they are interested in," she said.
She said the ban affected only schools, so there were ways girls wanting to play rugby could sidestep it.
"A young woman will still be able to do that, I understand, through their villages, even if this dictate is made by these schools," she said.
The Tonga Leitis Association, which represents the nation's transgender community, wrote to the education ministry urging a rethink.
It labelled the directive "disrespectful and discriminatory", saying it sent the wrong message to girls wanting to participate in sports.
"We kindly remind you that what lessens the dignity of women is telling them what they can and cannot do based on their biological sex," it said.
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