"They have been getting away with this for years, along with China and others," Trump said in a tweet, noting a weaker euro would make it "unfairly easier for them to compete against the USA."
Trump later highlighted gains in the German DAX, attributing the move to Draghi's comments. "Very unfair to the United States," he said.
Earlier in the day, Draghi said the euro zone's central bank would announce further stimulative measures if the economic situation does not improve. "In the absence of improvement, such that the sustained return of inflation to our aim is threatened, additional stimulus will be required," he said.
Draghi's comments sent the euro sliding against the dollar. At 10:29 a.m. ET, the euro was down 0.3% at $1.1187.
Trump has criticized efforts by other central banks to devalue their currency. In an interview with CNBC's "Squawk Box" on June 10, he said the U.S. needs a "fair playing field" against China's weaker yuan. That currency hit its 2019 lows against the dollar earlier this month. Trump said the yuan's declining value is mitigating the effect of U.S. tariffs on Chinese goods.
Trump has also gone after the Federal Reserve multiple times, calling for more stimulative policy measures. In the "Squawk Box" interview he said the Fed has been "very, very disruptive to us." The Fed raised rates four times in 2018.
He added in an ABC News interview that aired Friday that the Dow Jones Industrial Average would be "10,000 points higher if the Fed didn't raise rates.
The central bank will kick off a two-day monetary policy meeting on Tuesday. Investors are not expecting any policy changes after the event, but they will look for clues about potential rate cuts later this year.