The cartoon depicts Germany's finance minister in a Wehrmacht uniform saying "we insist on the soap from your fat... We are prepared to discuss the fertiliser from your ashes".
The headline reads, "The negotiation has begun", referring to the talks the new Syriza-led government in Athens is holding with its eurozone partners on debt relief and economic reforms.
The artist who created the cartoon in Sunday's Avgi newspaper, a pro-Syriza party daily, should be "ashamed", said Schaeuble's spokesman.
"I will also make use of this freedom of expression, and on a very personal basis I say: this caricature is vile and the artist of this caricature should be ashamed."
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The cartoon's publication comes amid growing tensions between Greece and Berlin, fuelled by Athens's claim that it should receive reparations from Germany for the damages wrought by the Nazis during World War II.
Contacted about the issue, Avgi cartoonist Tassos Anastassiou declined to comment on the German complaint.
But in answering another complaint from the Greek Israelite community of Athens, Anastassiou on February 11 had insisted he meant "no insult or disrespect" to Holocaust victims.
"There was no intention to insult or disrespect the most savage and repulsive moment in modern history: the Holocaust," Anastassiou said.
The Greek newspaper, which has a daily circulation of only about 1,800, published another cartoon of Schaeuble in its Friday edition, also wearing a German army uniform.
Germany has been the strongest opponent of Greek Prime Minister Alexis Tsipras's plans for an overhaul of its huge loans programme.
And the countries have clashed over reparations, which Greece has repeatedly said it has a "moral obligation" to claim, despite a firm "no" from Berlin.