The deterioration in relations between the two sides has worked against the euro, which is used by 18 EU countries. The crisis in Ukraine has given traders an opportunity to sell the euro, which had been at multiyear highs against the dollar despite the muted economic recovery in the eurozone and low interest rates.
The single currency fell a further 0.4 percent Tuesday to $1.3464, its lowest level since last November. Analysts say the prospect of a protracted standoff between Europe and Russia could prompt further falls in the currency.
"Tougher economic sanctions on Russia would more than likely continue to entice investors towards selling the euro," said Jameel Ahmad, chief market analyst at FXTM.
Over the past few months during the Ukraine crisis, the EU has appeared reluctant to impose crippling sanctions on Russia, partly because many countries such as Germany stand to lose business. Many parts of the EU are also heavily dependent on Russian-imported gas.
The scale of the Malaysia plane disaster has fueled speculation across financial markets that the EU will target Russia's wider economy as well as individuals if Moscow doesn't help calm the crisis.
That could have an impact on the European economy but most analysts think Russia, whose economy is stagnating, stands to lose a lot more.
"The biggest loser from all of this in economic terms will surely be Russia herself," said Julian Jessop, chief global economist at Capital Economics. "Even if sanctions are not tightened further and outright recession is avoided, growth will be held down by the growing reluctance of Western companies and banks to do business with what risks becoming a pariah state."
The fall in the value of the euro will likely be greeted in eurozone's capitals and especially by policymakers at the European Central Bank. Over the past few months, there have been concerns that the high value of the currency would weigh on the economic recovery by making eurozone exports more expensive, and keep inflation at too low a level by making imports cheaper.
Andrew Wilkinson, chief market strategist at Interactive Brokers, said the fall "might not upset the ECB, whose members are plausibly scratching their heads at the currency's resilience."