In an interview published today in the Financial Times, Juncker said he communicated his concerns during Vice President Mike Pence's visit to Brussels last month, during which he also expressed surprise over Trump's support of Brexit.
The US president has said that Britain's vote to leave the European Union was a good idea and that other countries would likely follow suit.
"I told the vice-president, 'Do not say that, do not invite others to leave, because if the European Union collapses, you will have a new war in the western Balkans'," Juncker told the paper.
"If we leave them alone- Bosnia-Herzegovina, Republika Srpska, Macedonia, Albania, all those countries- we will have war again," Juncker warned.
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Since the war in Bosnia ended in 1995, the country has been split along ethnic lines into two semi-independent entities- the Serbs' Republika Srpska and the Muslim-Croat Federation.
Bosnia and Herzegovina, along with Macedonia, Serbia, Montenegro, Kosovo, Slovenia and Croatia were all once part of the former Yugoslavia. Albania was always an independent state.
Last month, EU foreign affairs chief Federica Mogherini gave a similar warning, telling Washington not to "interfere" in European politics, saying: "Europeans feel and believe that their interest are better protected and promoted through our union."
According to media reports at the time, Trump has tipped businessman Ted Malloch as the next US ambassador to the EU.
Malloch has reportedly ruffled feathers with anti-EU comments, saying Brexit was a harbinger of the EU's eventual disintegration, according to the German and British press.