The arrangement was the result of dialogue between parents and teachers at the school, who held meetings with representatives from Norway's Refugee Board (flyktningetjenesten) and interpretors, according to Nordlys.
"If [parents] wish for their daughters to wear burkinis, bought with their own money, then that is okay, but they must having swimming lessons in the same way and together with all the others," Espen Hay, head teacher of Finnsnes School, told Nordlys.
"We made it clear to parents that religion does not provide exemption for participation in swimming lessons. It is important for us that no students miss out on the opportunities everyone else has," Hay continued.
The school hopes that the agreement will boost attendance of swimming classes.
"The Education Act [Opplæringsloven] sets out requirements for what must be learnt at school. Subjects or activities can not be rejected by children or parents or even by me as head teacher.
"Just as you can't not show up to mathematics because you don't like it, you must take part in swimming lessons," the Finnsnes School head continued.
A swimming club in neighbouring Denmark recently hit headlines after introducing separate swimming sessions for Muslim girls. The director of the club in Copenhagen called the move a "recipe for integration" after membership numbers soared.
But burkinis in normal swimming lessons - allowing all children to swim together - should be a natural sight, says Kristin Walseth, associate professor at the Faculty of Education and International Studies at Oslo and Akerhus University College.
"It is clearly an excellent initiative to get more students to attend swimming," said Walseth, who has a Ph.D. in sports, Islam and integration, to Nordlys.
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"The initiative should be completely uncontroversial. On a practical level, it is actually better than swimmin in normal clothes, since the burkini is made of the correct material for use in swimming pools," Walseth continued.
"Many Norwegian travel enthusiasts have surely seen lots of people using this garment in countries where they are on vacation. It's just a swimming suit that covers a bit more," the professor said.
Ministry of Education guidelines state that policy regarding cases such as the burkini is up to individual municipalites to decide, writes NRK.