In a joint statement, the association and the Stockholm-based Imam Ali (AS) Islamic Center pledged efforts to prevent such offensive moves.
They noted that they have made contacts with related officials, including police and culture ministry to express disgust at the move that was aimed at hurting the feelings of Muslims in Sweden and elsewhere.
The statement also called on Muslims to counter the offensive move with prudence and avoid providing pretexts for ill-wishers.
A copy of the Quran was burned by supporters of racist Danish leader Rasmus Paludan, the leader of the anti-Islamic group Tight Direction (Stram Kurs), during a rally in Malmo last month.
The rally was marred by violence, which left several police officers injured. At least 10 people were arrested. Police also banned Paludan from entering Sweden for two years.