The remarks came after a person identified as Salwan Momika burned a copy of the Muslim holy book under police protection in front of a Stockholm mosque on Wednesday.
The desecration was timed to coincide with Eid al-Adha, one of the major Islamic religious festivals celebrated by Muslims worldwide.
"Manifestations of racism, xenophobia and related intolerance have no place in Europe," Nabila Massrali, the EU spokesperson for foreign affairs and security policy, said in a statement.
"The EU joins the Swedish Ministry of Foreign Affairs in its strong rejection of the burning of a Quran by an individual in Sweden. This act in no way reflects the opinions of the European Union."
She added: "It is even more deplorable that such act was carried out on the important Muslim celebration of Eid al Adha."