The former Luxembourg prime minister became president in 2014, with the support of 26 out of 28 EU governments.
But the UK was fiercely opposed to his election, as he advocated deeper EU integration.
In his interview with broadcaster Deutschlandfunk (in German), Mr Juncker said he had had "a fine election campaign" in 2014, "but there won`t be a second one, because I won`t be putting myself forward as a candidate for a second time".
He also said he thought the EU`s remaining 27 members could struggle to stay united as they negotiated with Britain over the terms of its exit from the EU.
"Do the Hungarians and the Poles want exactly the same thing as the Germans and the French? I have serious doubts," he said.
The European Commission is responsible for proposing new EU legislation, drawing up the EU`s budget and supervising EU funding.
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