The minister, Omran al-Zoubi, said in a rare comment from Damascus, that the migrants are mostly fleeing from areas held by rivals of President Bashar Assad's government, including the Islamic State group.
His remarks, carried by state media, say European countries, "which sent terrorists" to Syria and imposed economic sanctions on the Syrian people, must take responsibility for their anti-Syria policies.
European countries have been harsh critics of Assad's government and thousands of fighters from around the world, including Europe, have come to Syria to fight with extremist groups such as the IS against government forces.
In some cases, Europeans who went to Syria returned home to stage deadly attacks — such as the French suspect in a 2014 attack on a Jewish museum in Belgium, who had come back from fighting with extremists in Syria.
Authorities around Europe have repeatedly warned of the threat posed by the return of Western jihadis, trained in warfare in the Mideast. France counts at least 1,200 citizens in the war zone in Syria — headed there, returned or dead. Both the Islamic State group and al-Qaida have threatened France, home to Western Europe's largest Muslim population.
But Damascus is not forcing anyone out, al-Zoubi said. "Any Syrian abroad can return to his country anytime he wants," he added.