Mayor Michel Amiel of Pennes-Mirabeau, near Marseilles, announced he had discussed the proposed party with the Speed Water Park venue with regards to the “extreme ideological positions” he believed the organisers were taking.
A joint decision was made to call off the event in an effort to “calm the situation” and preserve public order after a heated reaction from residents, according to the Local.
Muslim community group Smile 13 had organised the event for September 10 as an opportunity for women to swim in private for eight hours while wearing the burkini swimming costume.
Shortly after posters went up around Pennes-Mirabeau, Mr Amiel announced he intended to take up a city bylaw to prohibit the event “on the grounds it is likely to cause public disorder”.
The idea for the party particularly outraged local right-wing politicians, who argued it contravened legally-binding French secular values and promoted “communalism”.
Following the cancellation, Smile 13 confirmed one of its members had been sent an envelope containing bullets, and condemned those who had sought to threaten the event.
The group wrote a lengthy Facebook post criticising the “narrow-minded polemicists and politicians” who had attacked the party, before appearing to delete its Facebook account.
The statement continued: “It's with astonishment and regret that we have noted the extent of this controversy.
"The situation has become surreal, from insults, incessant journalist requests, and death threats to members of the team.
“Our group is an open and tolerant one, including women from different backgrounds regardless of their religious and clothing choices.”
Smile 13 added it planned to take legal action against those who had sent the death threats.
Meanwhile Mr Amiel told a local radio station: “The manager of the pool had not considered the sheer emotion that organising this event could generate.
“We saw the reactions on social networks that were completely outrageous, Islamophobic, xenophobic and racist, which I totally condemn but given the circumstances we have to cool things off.”
In the wake of the announcement, local right wing politician Valerie Boyer tweeted: "It is a victory for our values. We must never give in.
"I will not stay silent in the face of those who refuse assimilation!"
Around 2,000 of France’s 5 million Muslim citizens are thought to wear full veils, and the country has had a difficult history when it comes to Islamic dress.
France's swimming pools usually have strict rules forbidding people swimming in certain clothes and the 2004 law banned the wearing of the Muslim headscarf and other religious signs in public buildings.
The launch of the burkini by certain French brands in March this year was attacked in some circles, with some politicians describing the introduction of the swimming costume as “irresponsible”.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies