Italian authorities had banned fans of the German club from attending the match due to concerns about possible violence, but many Eintracht supporters made the trip to Italy anyway.
A bus carrying a group of Eintracht fans was hit by a barrage of fireworks and other objects, kicking off the incidents and havoc.
Some German 'ultras dressed in black with their faces covered threw glass bottles at a closed bar in the city's Piazza Bellini.
Police officers were stationed outside a hotel on the Naples seafront where a number of Eintracht supporters were staying.
Despite this, running battles between opposing fans broke out Wednesday with objects thrown by German fans and people wearing motorcycle helmets.
A police car was set on fire while another two were damaged.
Several rubbish containers were overturned.
Stones were thrown at a bus containing German fans.
Locals ran for cover or huddled in their home for safety.
Naples Mayor Gaetano Manfredi called the damage caused by the German fans "crazy and unacceptable", while the right-wing League party said the German government should pay to repair the damage.
Manfredi said he had met the German Consul General in Naples and they both condemned the violence.
UEFA President Aleksander Ceferin on Tuesday criticised the decision to stop Frankfurt residents attending the match and threatened to move games away from clubs' home grounds if away fans are banned in future.
Napoli won the match 3-0, 5-0 on aggregate.
ANSA
