The eight were later banned from the Naples stadium for between five and eight years, police said.
Six police officers were injured in the violence on Wednesday evening, according to Alessandro Giuliano, who is responsible for public safety in the southern Italian city.
The first clashes occurred in the historic centre in the afternoon, and continued after the match, an easy 3-0 win for Napoli which took them through to the Champions League quarterfinals for the first time.
Smoke bombs and flares, chairs, bottles and metal poles were thrown at police, who responded with tear gas. Later, Napoli fans were filmed by Italian media throwing objects at buses carrying Eintracht fans.
Police were in the process of identifying 470 German fans who stayed in the city, and were scouring images to establish those responsible for the disorder, Giuliano told a press conference.
Dozens of supporters of Atalanta, who have a history of conflict with Napoli fans, joined forces with supporters of the German side.
Naples mayor Gaetano Manfredi condemned the "unacceptable" violence, while opposition politicians have questioned the government's handling of the situation, notably by Interior Minister Matteo Piantedosi.
Napoli player Juan Jesus said the disorder was "bad for the city, and bad for soccer".
"Because people come, then destroy, then leave, it's not a good thing. It's not possible to still see this in 2023, we are sorry to see these scenes," he said.
Eintracht Frankfurt board member Philipp Reschke also expressed his dismay.
"We deeply regret the events that have taken place here. There is absolutely nothing to justify this violence... it is unacceptable," Reschke said on Thursday before the team boarded a flight back to Frankfurt.
"It harms football, it harms Eintracht Frankfurt and it harms our efforts to stick up for fans who want to watch a game without restrictions in the stadium."
The German supporters had travelled to southern Italy even though Eintracht decided against selling tickets for the away section in Naples for the second leg of the last-16 tie.
The Frankfurt club opted not to take up their allocation after the Naples prefecture decided on Sunday to ban residents of the German city from buying tickets.
An earlier Italian ban on Eintracht fans who lived anywhere in Germany was overturned.
Sunday's decision came after violence in the first leg that was won 2-0 by Napoli in Frankfurt, which led to nine people being taken into custody.
Eintracht fans have been under close surveillance by European governing body Uefa since the pitch invasion which greeted the club reaching the final of the Europa League, which they won by beating Scottish club Rangers.