The local reception centre, built to house fewer than 400 people, was overwhelmed with men, women and children forced to sleep outside on makeshift plastic cots, many wrapped in metallic emergency blankets.
Tensions broke out on Wednesday as food was being distributed by the Italian Red Cross, which runs the facility, causing police to intervene.
Some young men later left the overcrowded centre and went into Lampedusa’s old town centre, where an AFP photographer found some of them queuing for ice cream.
Several said they were hungry. Few had any money, and some restaurants turned them away. But other establishments offered food for free, or residents and tourists paid for them.
Located just 90 miles (around 145 kilometres) off the coast of Tunisia, Lampedusa is one of the first points of call for migrants crossing the Mediterranean.
Days of fine weather has seen a surge in arrivals in recent days, with more than 5,000 people arriving in Italy on Tuesday alone, according to interior ministry figures.
Most are picked up at sea from rickety boats by the coastguard, which brings them to Lampedusa port.
But many do not make it that far. More than 2,000 people have died this year crossing the sea between North Africa and Italy, according to the UN migration agency.
The latest victim was a five-month-old baby, who reportedly fell into the water early on Wednesday as part of a group being brought to shore.
For years, Lampedusa has struggled to cope with the numbers arriving, with humanitarian organisations reporting a lack of
water, food and medical care.
The Italian Red Cross took over in June promising to offer a more “dignified” welcome, but admitted this week it was having difficulty with the surge in arrivals.
It reported more than 7,000 people at the hotspot on Wednesday evening, a figure that resulted in “management problems, even if caused by a small number of people”.
Some 5,000 people were due to be transferred by the end of Thursday to Sicily, where there are larger processing facilities.
“The situation is certainly complex and, gradually, we are trying to return to normality,” Francesca Basile, head of migration for the Italian Red Cross, said on Thursday morning.
She said that “despite the critical situation, we still tried to distribute cots to people to prevent them sleeping out in the open”.
“We provided everyone with food and distributed dinner last night and today too everyone will receive what they need.”
Italy’s hard-right government allocated 45 million euros to Lampedusa earlier this month to help the island better manage the migrant situation.
But Prime Minister Giorgia Meloni, elected one year ago on a pledge to end mass migration, is calling for help from the EU.
Almost 124,000 migrants have arrived on Italy’s shores so far this year, up from 65,500 in the same period last year.
The numbers have yet to pass those of 2016, however, when more than 181,000 arrived during a surge in irregular migration into Europe, many of them Syrians escaping war.