Grillo's blog carried a photoshopped picture of Schulz as a Nazi whipping Italian Prime Minister Matteo Renzi and his post said that the European Parliament's German president "has no shame in talking crap".
Grillo said Silvio Berlusconi was "not completely wrong when he called him a kapo", or concentration camp guard, recalling an infamous speech made by the then prime minister to the European Parliament in 2003.
Grillo called Schulz a "sturmtruppen" - a reference to a comic book series - and said he was a "krapo", a combination of the word "kapo" and "crapun" - a dialect word meaning "big head" that was used to refer to Italian fascist dictator Benito Mussolini.
"Krapo Schulz said Grillo is just wind. He's partly right. The Five Star Movement is a wind from the south that is about to land in Brussels. Krapo should hold on tight - it could be a hurricane," Grillo's blog said.
The Five Star Movement protest party is predicted by opinion polls to garner around a quarter of Italy's vote in the May 25 European Parliament elections, coming in second after Renzi's centre-left Democratic Party.
Grillo's party is calling for a referendum on whether Italy should stay in the euro and for the abolition of the "fiscal compact" - a series of debt reduction targets agreed during the eurozone financial crisis.
Schulz in an interview with the Corriere della Sera daily on Sunday accused Grillo of having an "authoritarian tendency" and likened him to Soviet leader Joseph Stalin and Venezuelan president Chavez.