The case, which occurred last year but was made public by broadcaster SRF on Monday, involved two sisters, aged 12 and 14.
Speaking to the broadcaster, Stefan Wehrle, president of the naturalization committee involved in the decision, said young people wishing to become Swiss citizens must prove they are meeting the requirements of the Swiss education system.
Since swimming lessons are compulsory in Basel's schools – and in many other places in Switzerland including Zurich and Bern – failing to attend means a student is not meeting requirements.
“Whoever doesn't fulfill these conditions violates the law and therefore cannot be naturalized,” Wehrle said.
Swiss courts have previously refused the pleas of several Muslim families to exempt their children from swimming lessons, saying integration comes before religion.
And authorities in Basel have dished out fines to the parents of Muslim children who refuse to participate in swimming lessons.
However this is the first time a citizenship application has been refused on such grounds, making it a case that could set a precedent in the canton, said the broadcaster.
Proof of integration is a vital part of becoming naturalized in Switzerland, a process involving cantonal and communal authorities including a resident-led committee.
The perceived lack of integration of Muslim children in Swiss schools has frequently made headlines of late.
Earlier this year two Muslim schoolboys in Therwil refused to shake hands with their female teachers on religious grounds, causing uproar across the country.
Their school initially exempted them from shaking hands, before authorities ruled they must shake or face a fine.
On Monday SRF said the two girls in the swimming case also refused to shake hands with teachers.
But since handshaking is not a compulsory part of education that was not a factor in the decision, said the broadcaster.
The Therwil boys have also applied for citizenship, and a decision is still pending.