The Social Democrat leader then said it did not matter that Merkel and he were in the middle of an election campaign, as "the Chancellor represents all of us at summits like these, and I reject with outrage the way this man takes it upon himself to treat the head of our country's Government".
"That is unacceptable," Schulz said.
He had made a similar comment yesterday shortly after Merkel's remarks. "A stronger co-operation of European countries on all levels is the answer to Donald Trump," Schulz told the public broadcaster ARD. Today, he tweeted in German, English and French that the "best response to Donald Trump is a stronger Europe".
Such comments suggest that Trump's reputation in Europe may end up influencing the continent's politics in unexpected ways.
Although the possibility of a Schulz chancellery has become less and less likely after poor showings by the Social Democrats in recent regional elections, the centre-left's animosity towards Trump is broadly shared by many German voters.
In a poll conducted in February, 78 per cent of Germans said they were "very concerned" about Trump's policies - almost 20 per cent more than those who were worried about the politics of Russian President Vladimir Putin.
Characteristically, Schulz has taken a more direct tone in his criticism than the soft-spoken Merkel, calling Trump's policies "un-American" in late January.
Notably, he has pushed back on long-standing US demands for Germany to spend 2 per cent of its gross domestic product on defence - something Trump pushed during last week's meeting of the leaders of the North Atlantic Treaty Organisation.
However, while the Christian Democrats were beneficiaries of a short-lived "Trump bump" after the 2016 US presidential election, Merkel also may have found ways to use Germans' animosity toward Trump to her advantage.
Thanks to a quirk of scheduling, before she met Trump in Brussels last week, she spent a morning with former US President Barack Obama, who is still broadly admired in Germany.
After Merkel's comments about Trump at the beer hall, she received applause for a whole minute. The next day, her spokesman reiterated her intent. "The Chancellor's words stand on their own," Steffen Seibert said during a news conference. "They were clear and comprehensible."