Other demonstrators sat on the dock refusing to move, while a small group attempted to assault the ship.
Protests by residents were also reported near a waste disposal plant where the rubbish is believed to be going.
"It's been a busy night," Silvio Saffioti, the head of the fire brigade in the Sardinian capital, Cagliari, said.
"We were called out 25 times to put out fires in 48 [rubbish containers] and three burning cars."
Collectors in Naples and its surrounding Campania region stopped picking up rubbish before Christmas because there was no more room for it at dumps.
Prodi plea
Romano Prodi, the Italian prime minister, urged other regions to accept some of the rubbish as part of the measures he announced to combat the problem earlier this week.
Officials in Sardinia agreed to help and a cargo boat arrived in the port of Cagliari on Friday evening, with the regional government saying it could accept more in the coming days.
"The immediate willingness of our region [to accept the rubbish] is allowing authorities to show the first results in the streets of Naples, and at the same time, to plan for the disposal of a good part of the garbage from the areas around Campania," Cicito Morittu, a regional environment official, said.
The region has long been plagued by such rubbish crises.
Dumps are already packed to overflowing, and local communities have blocked efforts to build new ones, citing health risks.
Officials and residents say the crises stem from the Neapolitan mafia's control of rubbish disposal and the government's inability to fight it or guarantee safe waste treatment.
On Thursday, the interior ministry warned that it was intensifying its investigation to identify violent protesters who had clashed with police and firefighters in recent days in a bid to prevent the Pianura dump near Naples from reopening.
In a statement issued after a high-level meeting with law enforcement agencies, the ministry said that rapid-response police patrols would be intensified to cope with any future violence by protesters