Speaking in Rome on Friday, the German deputy said, "The forces unleashed by the crises we are facing are driving us apart, not bringing us closer together: national self-interest, renationalisation and particularism are gaining ground.
"There can be no doubt that the refugee crisis represents a defining challenge for Europe. At no time since the Second World War have so many people around the world been fleeing violence and terror."
The Socialist MEP went on, "Unscrupulous populists, who have no solutions to offer, are taking advantage of the situation to prey on the fears of ordinary people. Fear may be understandable, but it is a bad policymaker."
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Schulz was speaking in the Vatican on the occasion of the award of the EU's Charlemagne Prize to Pope Francis.
The Charlemagne Prize, said Schulz, is a prize awarded by the citizens of Aachen, a city situated in his home region.
Schulz, alluding to Donald Trump's pledge to build a wall between the U.S and Mexico, added, "The people who, 25 years after the fall of the Iron Curtain, want to put up new walls and fences in Europe and in so doing jeopardise one of Europe's greatest achievements, freedom of movement, have clearly learnt nothing from history.
"Surely nobody really believes that the people fleeing the brutal violence of Islamic State or the bombs of the Assad regime would be deterred by walls and barbed wire."
In an indirect reference to the Brexit campaign in the UK, he said, "People who claim that nation states would do better to go it alone have lost touch with reality. Surely nobody really believes that, if our continent were to fragment, we Europeans, and our unique social model, could survive in an ever more globalised and interconnected world."
Speaking at the same event, European Council President Donald Tusk said, "We were and will be Europeans. I would not like this to be just a statement of geographical nature, nor an exclusively political declaration. It is also, and perhaps foremost, a statement of axiology and metaphysics. In a sense, Europe is an article of faith."
The former Polish Prime Minister, who accompanied Schulz and European Commission President Jean-Claude Juncker at the ceremony, added, "Why should we be proud of Europe? Why is it worth our concern, and - if need be - our protection and defence? It is because the spirit of love and freedom is still present."