Although only two people were expected to take part, the organisers said they would tear up and burn the Koran.
Sweden sought NATO membership in the wake of Russia's invasion of Ukraine last year.
But alliance member Ankara has held up the process, accusing Sweden of harbouring people it considers terrorists and demanding their extradition.
While Swedish police have rejected several recent applications for anti-Koran demonstrations, courts have overruled those decisions, saying they infringed on freedom of speech.
Prime Minister Ulf Kristersson said at a press conference on Wednesday he would not speculate about how the approved Koran burning could affect Sweden's NATO process.
Persons:
Ulf Kristersson, Kristersson, Momika, Rasmus Paludan, Paludan, Louise Breusch Rasmussen, Marie Mannes, Johan Ahlander, Terje Solsvik, Peter Graff, Angus MacSwan
Organizations:
Police, NATO, Islam, Atlantic Treaty Organization, Swedish, Thomson
Locations:
STOCKHOLM, Stockholm, Turkey, Sweden, Ukraine, Ankara, Danish, Turkish, Saudi Arabia, Jordan, Kuwait, Copenhagen