The euro tumbled as low as $ 1.3609, its lowest level since October 12, before recovering to $ 1.3697 at 0330 IST, down from $1.3851 late Monday.
It was a big drop from the $ 1.42 level struck last Thursday, following the EU summit's reaching a comprehensive deal to resolve the months-long crisis in the euro zone, beginning with a new Greek debt reduction and austerity deal.
"This throws all the summit's deliberations up in the air, even though they were considered lame in the first place," said David Morrison of currency specialist FX360.
"In consequence, investors are rushing to reduce their risk exposure across the board and fleeing into the relative safety of the dollar and US Treasuries."
The euro fell to 107.29 Japanese yen, down from 108.28 yen, while the dollar rose to 78.34 yen from 78.16.
The dollar was almost unchanged at 0.8869 Swiss francs. The British pound fell to $1.5950 from $ 1.6073.
While the euro zone crisis will continue to drive markets -- France and Germany have already called another emergency summit to deal with the Greek issue -- traders will also be watching whatever comes out Wednesday from the meeting of the US Federal Reserve's policy board.
While few expect any overt policy decisions -- interest rates should be kept at the ultra-low levels -- some anticipate signals in the language the Fed uses to indicate the medium-term direction of monetary policy.