"I think on the day people will look to re-sell 1.1250/60 or less," said Stephen Gallo, European head of FX strategy with Bank of Montreal in London.
"The fact that the ECB's QE programme has already been announced is positive for credit spreads and limits the damage on the euro. That and positioning were probably responsible for the bounce from the lows around $1.11."
The euro has lost 10 full cents against the dollar since the start of the year and, at $1.11, more than 4 cents since the ECB's announcement last week.
It fell to as low as 130.160 yen, its lowest level in 1-1/2 years, before it bounced back to 131.500. Against sterling, it hit a seven-year low of 74.06 pence.
Market participants saw the risk that euro selling would pick up later in the day if Syriza reiterates a tough stance for negotiations with the "Troika" of the European Central Bank, the International Monetary Fund and the European Commission.
Such a scenario could trigger a test of $1.10, where large options lay, according to several research notes.
"The absolutely dominant view is that we are heading towards parity to the dollar, the only question is how fast," said a senior dealer with one large international bank in London.
"The only buyers are the short-term speculative players caught short at the wrong level."
Read MoreEuro, dollar to hit parity by 2016: Economist
Some analysts, however, said the long-term impact may be more nuanced as most investors expect Tsipras, at the end of the day, to work with the European Union and other international lenders.
"Usually politicians say populist things before an election. So now the question is how much they are going to stick to the promises made to the Troika," said Ayako Sera, market strategist at Sumitomo Mitsui Trust Bank.
ECB board member Benoit Coeure said in a newspaper interview published on Monday that the European Central Bank would not take part in any debt cut for Greece. He also said the euro would have to stabilise at some stage.
"The market was largely anticipating a (Syriza) victory," said Sebastien Galy, senior foreign exchange analyst at Societe Generale in New York.
"At the moment, the market believes that if there is any (debt) restructuring it would only involve the official sector and for now, the possibility of Greece leaving the euro zone even with the incoming government is small," he added.
Among other major currencies, the Aussie sank as low as $0.7850, its lowest since mid-2009, while the kiwi fell to a more than three-year trough of $0.7407.