Italy has built two reception centres in Albania under its controversial programme, which aims to deter irregular arrivals to Italy but has been criticised by rights groups who say it restricts migrants' right to asylum.
The Libra, an Italian navy ship, docked at Shengjin, Reuters footage showed.
Sixteen migrants were escorted into a newly built processing centre at the port, ringed by a high metal fence and adorned with Italian and EU flags.
Rising tension in Europe over migration issues has resulted in many countries, including Germany and Poland, proposing or adopting tougher policies.
The United Kingdom's previous government had planned to deport asylum seekers to Rwanda, although Prime Minister Keir Starmer scrapped the plan after taking office in July.
Italian Prime Minister Giorgia Meloni said this week that her country was setting an example for the rest of Europe with the Albanian scheme.
Fifteen European countries have taken an interest in the scheme, Interior Minister Matteo Piantedosi said in parliament in Rome, without naming them.
Earlier, Czech Prime Minister Petr Fiala said the Italian scheme may serve as a model.
Interest from others "is the greatest proof of the innovative value of the initiative that aims to fight illegal immigration without affecting the guarantees of people's fundamental rights," Piantedosi said.
However a small group of protesters gathered at the port on Wednesday.
"The European dream ends here," one banner read.
"These immigrants who have done long, dangerous journeys to make it to Europe are now rerouting to Albania so that they will go back to their home countries ... It's ending for us (the concept of) Europe as a place of democracy, of values, of human rights," Arilda Lleshi, an Albanian human rights activist, said.
The group of migrants taken to Albania comprised 10 Bangladeshis and six Egyptians picked up at sea on Sunday aboard boats that had set sail from Libya.
After processing in Shengjin, they are scheduled to be taken inland to the village of Gjader, a 15-minute drive away, where they will be accommodated until their papers are finalised.
They will then be sent to Italy if their asylum request is granted, or to their home country if rejected.
The facilities in Shengjin and Gjader will be staffed by Italian personnel.
Under the deal, the total number of migrants present at one time in Albania cannot be more than 3000.
Italy has said only "non-vulnerable" men coming from countries classified as safe would be sent to Albania, to a limit of 36,000 migrants a year.
At present there are 21 such countries on the Italian list.
Last year, 56,588 migrants arrived in Italy from just four of them - Bangladesh, Egypt, Ivory Coast and Tunisia.
Most abscond from reception centres and head to wealthier northern European countries.
Marta Welander, EU Advocacy Director at aid group the International Rescue Committee, said the new arrangements risked jeopardising the right to seek asylum no matter where a person comes from or how they arrive.
