The euro fell to a nine-year low against the U.S. dollar on January 5, and the Russian ruble lost ground as oil prices dropped as low as $50 per barrel, according to AFP.
The European currency hit $1.1864, its lowest level since March 2006, before recovering moderately.
The decline failed to spur a rally in European stocks, which fell sharply amid fears that Greece could soon leave the 19-nation eurozone.
U.S. crude oil dropped below $50 per barrel for the first time in five years, while benchmark Brent North Sea crude was selling for about $53 per barrel.
The ruble, which lost nearly half its value last year and dropped as low as 80 per dollar on December 16 before recovering, was back below 60 per dollar late on January 5.
Russia's energy-reliant economy has been hit by falling oil prices and Western sanctions imposed over Moscow's interference in Ukraine.