The victims were all slashed across the buttocks by thugs on scooters although none of them were seriously hurt.
The attacks were believed to be carried out by members of Napoli's notorious 'Ultras' group and raises fears for the safety of City supporters.
Hostile: Napoli fans lit flares and some of were thrown into the Bayern section
Roberto Mancini's side are due in the Italian port city for their Group A Champions League clash on November 22.
Four of the stabbings took place outside Napoli's San Paolo Stadium, while the other two happened near the city's main station. Flares were also thrown into the Bayern section by home fans inside the ground.
Pitch battle: Philipp Lahm of Bayern holds off Napoli defender Christian Maggio
Naples mayor Luigi De Magistris said: 'Sport is not compatible with violence. That is why I strongly condemn what happened.'
Several Liverpool fans were attacked when they attended a Europa League match in the city in 2010.
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