Mr Schulz, 61, who stepped down from his post in the Parliament in an attempt to take over from Angela Merkel as Chancellor, has been accused of trying to appeal to populist sentiment and that he was being like the US President.
Mr Schauble, of the ruling Christian Democratic Union (CDU), went on the attack against his opponent from the centre-left German Social Democratic Party (SPD) in an interview with the German weekly news magazine Der Spiegel.
Wolfgang Schauble has attacked Martin Schulz for his populist views
He said: “If Schulz calls upon his supporters to chant ‘Make Europe great again‘ then that’s almost literally Trump, almost word-for-word.”
He added that Schulz was acting in a “populist way”, adding that he should “think a little [bit more].”
He stated that in times where there was a surge in populist movements, politicians needed to be careful with their language.
Martin Schulz speaking to members of the SPD earlier this month
Mr Schauble said: "If Schulz allows his supporters to use the slogan 'Make Europe Great Again,' then he is Trump almost word-for-word."
“In a time when populism is seducing people the world over, politicians should not speak like Mr Schulz.
“If he wants to fight populism, as he claims, he should take note of these facts."
Wolfgang Schauble arriving for a Eurogroup meeting
Mr Schulz has expressed his dislike for the US President calling Mr Trump "dangerous to democracy" and accusing him of "playing with the security of the Western world."
In the same interview with Der Spiegel, Mr Schauble also scoffed at what he perceived as the SPD trying to promote Mr Schulz as a political underdog.
Wolfgang Schauble compared Martin Schulz to Donald Trump
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Mr Schauble said: “The man has sat in the European Parliament for decades, most recently as its President.
"If that's not part of the establishment, what is?"
Supporters of Mr Schulz were quick to retaliate, saying that the comments indicated just how out of touch the minister was with voters’ concerns.
Martin Schulz speaking at an SPD rally
SPD politicians accused Mr Schauble of "irrelevant" and "hysterical" criticism of their candidate, adding that the statement must have come from a panic in the CDU as Mr Schulz's popularity among German voters increases.
SPD deputy leader Ralf Stegner said: ”My advice to Mr Schauble is that he should say fewer things that show that he knows little about the reality of his fellow citizens.”
Germany's Finance Minister Wolfgang Schauble has attacked Martin Schulz
For the past four years, the CDU and SPD have been ruling together in a grand coalition after 2013 election results shut out the CDU's preferred coalition partner, the Free Democrats (FDP).
The German federal election will take place on September 24 this year.