Euro-dollar one-month implied volatility had hit record lows around 3.8% but started rising sharply in recent weeks and traded on Friday at 7.7%. It traded at 6.75% a week ago.
The euro has soared towards $1.13 this week, up from less than $1.08 last month.
Analysts say one source of the rise in volatility has been investors closing their carry trade positions, in which they borrow in negative-yielding currencies such as the euro and yen to buy higher-yielding assets in dollars or emerging markets.