Clinton is viewed as the candidate of the status quo, while there is greater uncertainty over what a victory for Trump might mean for U.S. foreign policy, international trade deals and the domestic economy.
Analysts said a Trump victory could throw the Federal Reserve off its presumed course of hiking interest rates in December. Investors awaited Wednesday's Fed statement for any new indications that a rate increase is likely at the U.S. central bank's December meeting.
"The market has built up some dollar longs and euro shorts in recent weeks, and with Friday's news increasing the uncertainty around the election outcome, we suspect market participants are cutting back" on those positions, said Vassili Serebriakov, FX strategist at Credit Agricole in New York.
The dollar index, which measures the greenback against a basket of six major rivals, fell more than 0.5 percent to its lowest level since Oct. 20 at 97.878. The index had gained 3.1 percent in October to mark its strongest month in just under a year.
The euro gained about 0.6 percent against the dollar to a more than two-week high of $1.1046. The dollar fell about 0.9 percent against the Swiss franc to a more than three-week low of 0.9797 franc and dipped about 0.3 percent against the yen to a session low of 104.52 yen.
The Mexican peso fell about 1.3 percent against the greenback to 19.1102 pesos per dollar, its weakest level since Oct. 7.
A potential Trump victory has been viewed as a key risk for the Mexican currency given Trump's promises to clamp down on immigration and rethink trade relations.