"Please, don't give us lessons in human rights and democracy," the minister said, as he spoke to a crowd of some 200 Turkish government supporters gathered at the residence of their country's consul in the northern city of Hamburg.
The comments came after German local authorities banned rallies that Turkish officials were due to address to raise support among expatriate voters for a referendum in April on boosting President Recep Tayyip Erdogan's powers.
"Germany must not intervene in our elections and our referendum," he said.
"Those who want to say 'Yes' in the referendum are being blocked and that is not right."
Local authorities had called off a rally in Hamburg where Cavusoglu was due to speak, citing fire safety concerns.
Police said about 250 opponents of Erdogan gathered near the consulate, some of them brandishing signs that read "Dictator Erdogan -- Hayir," meaning "No" in Turkish.
Cavusoglu said he would meet Wednesday with his German counterpart Sigmar Gabriel, whom he called a "friend", at a breakfast in Berlin and visit a tourism fair.
Tensions have been rocketing between NATO allies Turkey and Germany over the past week after the cancellation of several rallies where Turkish cabinet ministers were due to whip up support for a "yes" vote in the April 16th referendum.
Erdogan escalated the crisis over the weekend, likening the cancellations to "Nazi practices," drawing a sharp response from Berlin.
He also warned Germany not to block him from making an appearance if he wished.
Chancellor Angela Merkel's office firmly rejected the Nazi jibe as "absurd and out of place".
Cavusoglu said the rally cancellations were "unacceptable" and reminiscent of practices in the run-up to World War II.
He criticised Germany and several other European countries including the Netherlands, where politicians including Prime Minister Mark Rutte have condemned Cavusoglu's plans to attend a similar rally in Rotterdam.
"We are in a state of great fear," Cavusoglu said. "If we cannot stop the advance of racist parties, Europe will head (back) to the pre-World War II period."
European Commission President Jean-Claude Juncker Tuesday condemned Erdogan's "Nazi" comments in an interview with Luxembourg's RTL television.
"I am surprised by what I hear from Turkey. When the Turkish president and his foreign minister say that today's Germany is worse than Nazi Germany, I can't accept it," the former Luxembourg prime minister said.
"Our parents and grandparents lived through the Nazi occupation," said Juncker, who was born in 1954.
Turkish EU Affairs Minister Omer Celik spoke Tuesday with Michael Roth, state secretary at Germany's foreign ministry, sources in Celick's ministry said.
"Turkish-German relations are not local authorities' responsibility but that of the German state," Celik told Roth, according to the sources.
"We believe this is a systematic obstacle to our government."
Germany is home to a sizeable Turkish community, with some 1.4 million able to vote in Turkey -- a potential electoral goldmine in the Erdogan government's campaign to create an executive presidency.
Cavusoglu accused countries "which we deem as friends" of openly taking sides, slamming it "unacceptable" and "embarrassing".
Turkish-German ties have been strained since a vast crackdown launched by Ankara after a failed coup bid to oust Erdogan in July 2016.
Mass detentions have alarmed Europe, which has urged Ankara to respect freedoms. Critics say the clampdown has targeted opponents of the government, not merely coup-plotters.
Adding to the acrimony Tuesday, Turkish Economy Minister Nihat Zeybekci said he had opened a case against German newspaper Bild for "seriously insulting" Erdogan and himself in a report.
The arrest of Deniz Yucel, a correspondent for Germany's Die Welt newspaper, has also sparked an outcry in Berlin after he was charged in Istanbul with spreading terrorist propaganda and inciting hatred.