Draghi's swipe came after Mnuchin said this week that "obviously a weaker dollar is good for us as it relates to trade and opportunities".
Wanting to keep all options on the table, Draghi is likely to signal a concern about the rapid rise in the currency but will maintain that it is not a policy target, hoping to strike a balanced message until policymakers are ready to unveil their blueprint for winding down stimulus, economists said.
The euro is at a three-year high against the dollar.
Draghi went on to say: "The recent volatility in the exchange rate represents a source of uncertainty.with regard to its possible implications for the medium-term outlook for price stability".
Draghi's comments echoed those he made in September and which helped weaken the currency at the time. At today's meeting, the Governing Council of the European Central Bank decided that the interest rate on the main refinancing operations and the interest rates on the marginal lending facility and the deposit facility should remain unchanged - 0.00%, 0.25% and -0.40%, respectively. Official comments can however have an impact. The market was also waiting in anticipation for Draghi to make his press conference later in the day and a part of the market was expecting him to talk down the euro as it felt that the European Central Bank would be uncomfortable with the quick and unfettered rise of the euro against the other currencies, especially the dollar.
LIVE cricket score and updates, Australia vs England, 4th ODI at Adelaide
The final match in the series takes place tomorrow, the first sporting event at a new 60,000-seater stadium in Perth. Hazlewood and Cummins's opening spell reduced England to 8 for 5 in the seventh over.
"The ECB refrained from aggressively pushing back against the strength of the euro at their monetary policy decision.but also warned the US against opening a Pandora's box of competitive devaluation", said William Adams, senior worldwide economist at the PNC Financial Services Group.
This week's bank meeting, he said, did not discuss tapering bond purchases.
The purchases, already twice reduced, are set to run until the end of September and investors are betting on their end in the fourth quarter.
The purchases pump newly created money into the economy to raise inflation and growth in the wake of the 19-country eurozone's crisis over high debt in member states like Italy and Greece.
He spoke after the European Central Bank left its massive financial stimulus for the eurozone economy in place, opting not to rock the boat after Mnuchin's comments. Germany's Ifo index of business sentiment matched its record high in January, and surveys show business activity is expanding rapidly.