"I shouldn't say but I have to say it, I still don't have a smartphone," the 62-year-old head of the EU's executive arm said at a news conference in the Baltic state's capital, Tallinn.
"So I couldn't become prime minister of Estonia, this would be totally impossible," Juncker said alongside a smiling Estonian premier Juri Ratas.
He added that Ratas was aware of his lack of a smartphone, "which is why he sent me, like in the 19th century, a postcard inviting me to Tallinn."
His admission comes 10 years after Apple introduced the iPhone and launched a global smartphone boom.
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It puts him in good technophobic company among world leaders, including German Chancellor Angela Merkel, who still does not have a Twitter account.
But it stands in contrast with US President Donald Trump, a prolific Twitter user whose most recent outburst about a TV host's facelift sparked a backlash yesterday.
Estonia, one of the world's most digitally connected countries, said it would push digital issues as part of its six-month stint as president of the EU, which begins tomorrow.
Juncker said he counted on Estonia's "leadership" in the months ahead.
"Even without being a techie I know that our future is digital. Digital is the DNA of your country and it needs to become part of the European DNA," Juncker said.
But in the wake of a huge global cyberattack which spread from Ukraine to hit several countries this week, security was also a priority, he said.
Estonia was the first state to be hit by a massive cyberattack, in 2007, which paralysed key corporate and government web services for days.
Estonia blamed Moscow, which denied the charge.