Analysts warned the single currency could soon hit parity with the dollar as investors are spooked by a long-running banking crisis in Italy and the possibility of elections that could usher in anti-EU parties.
Matteo Renzi stood by his promise to resign after his attempt to change the constitution was overwhelmingly rejected in Sunday's poll, leading to fears about the future of one the eurozone's biggest economies.
"His defeat in the face of populist moves will spawn concerns over the rest of Europe," said Yunosuke Ikeda, chief currency strategist at Nomura Securities in Tokyo.
The vote comes as anti-establishment, populist movements are gaining ground globally, fanning worries about the world order. Last month Donald Trump won the US election and in June Britain voted to leave the European Union.
Yannick Naud, head of fixed income at Banque Audi (Suisse) SA in Geneva, told Bloomberg News: "There is now a possibility of the euro reaching parity to the dollar. Maybe not right away, but it is a possibility if there is certainty regarding new elections."
The news sent the euro tumbling to $1.0506 at one point, its weakest mark since March last year, before edging back up slightly.
The dollar also fell to 112.88 yen from 113.51 yen in New York Friday before recovering. The yen is considered a safe bet in times of crisis and turmoil.
Hong Kong-Shenzhen link
However, Nomura's Ikeda added: "But given the fact that this had been predicted beforehand, it's not a surprise in the same way as the Brexit vote or (Donald) Trump's election victory.
"As Prime Minister Renzi has now resigned, some investors might think all the bad news is out now."
Regional equity investors turned negative after a recent run-up fuelled by Trump's win, which many say could lead to stronger growth in the world's top economy.
Tokyo was down 0.5 percent, while Shanghai slipped 0.8 percent, Sydney also eased 0.8 percent and Seoul was 0.1 percent lower.
Hong Kong shed 0.2 percent and Shenzhen's Composite Index, which tracks stocks on China's second exchange, lost 0.6 percent as the worries over Italy overshadowed the start of an exchange link-up.
The tie-up, similar to one that kicked off between Hong Kong and Shanghai two years ago, is being touted as the latest effort by Beijing to prove to global investors that its capital markets are gradually opening.
But analysts sounded a note of caution pointing to a China slowdown, the weak yuan and expected US rate hikes.
Dealers are also keeping an eye on the US Federal Reserve after data showed the US saw another solid rise in jobs created in November, which will strengthen expectations it will hike interest rates this month and through next year.
Oil prices sagged after last week's surge in response to an agreement between key producers OPEC and Russia to cut output from next month. The surprise deal Wednesday sent crude flying around 15 percent last week.
Key figures around 0200 GMT
Tokyo - Nikkei 225: DOWN 0.5 percent at 18,331.04
Hong Kong - Hang Seng: DOWN 0.2 percent at 22,523.91
Shenzhen - Composite: DOWN 0.6 percent at 2,071.66
Shanghai - Composite: DOWN 0.8 percent at 3,218.38
Euro/dollar: DOWN at $1.0563 from $1.0670 Friday
Dollar/yen: UP at 113.82 yen from 113.51 yen
Pound/dollar: DOWN at $1.2690 from $1.2734
Oil - West Texas Intermediate: DOWN 57 cents at $51.11 per barrel
Oil - Brent North Sea: DOWN 62 cents at $53.84
New York - Dow: DOWN 0.1 percent at 19,170.42 (close)
London - FTSE 100: DOWN 0.3 percent at 6,730.72 (close)