The German diplomat said there was a “blame game” playing out between Brussels and the heads of EU member states, emboldened by the Brexit vote and eager to follow Britain’s example of “taking back control”.
Mr Schultz was one of many key political figures appearing on last night’s BBC documentary After Brexit: The Battle For Europe.
The programme examined the aftershock from the UK’s referendum result last year, and the huge surge in popularity of anti-establishment figures across the continent before and after the historic vote.
It studied the rise of Front National leader Marine Le Pen in France and Beppe Grillo’s Five Star Movement in Italy, plus the anti-migrant rhetoric of the Hungarian government, along with interviews with past and present EU officials.
Speaking to the BBC’s Europe editor Katya Adler, Mr Schultz conceded there was now a “real risk” the historic 60-year-old union, forged from the embers of World War II, could collapse.
He said: “The problem is that member states play that game: ‘There is that [European] Union, we have nothing to do with it, that union is playing against us’.
“That blame game is a virus which could lead to the end of the European Union.”
Mr Schultz, who stepped down as President earlier this year, cited leaders like Hungarian Prime Minister Vikto Orban as an example of the battle engulfing the EU.
Mr Schultz added: “I tried to keep it [the EU] together.
“There are people like Mr Orban, who argue against the European Union.
“If that is to continue, the risk that we fall apart is a real risk, yes.”
He also said it was “unthinkable” that Le Pen could win the French presidential election.
He said: “She will never win, I’m absolutely sure.”