Ansarullah spokesman Muhammad Abdul Salam in a post on Twitter condemned the insulting act by racists, Al-Maseerah reported.
He called on the Swedish government to take measures to prevent such events from happening again.
Abdul Salam added that Muslim countries should give a decisive message to Stockholm so that it would adopt the necessary measures.
Also, Yemeni political parties in a joint statement denounced the Quran desecration as a reprehensible act and a dangerous assault on Muslims and their sanctities.
On Thursday, Rasmus Paludan, the Danish leader of the far-right Stram Kurs (Hard Line) party, burned a copy of the Holy Quran in southern Linkoping in Sweden, according to media reports.
Paludan has also threatened to burn copies of the Quran during extremist rallies.
Following the provocation, protests have erupted in parts of the northern European country.