The plight of migrants constitutes "one of the crucial issues of our day, notably in the Mediterranean where nearly 13,000 men, women and children have perished in shipwrecks since 2013," said acting jury head Joaquim Chissano, former president of Mozambique.
Lampedusa, Italy's most southerly outpost, was the first port of arrival for thousands of migrants setting off from North Africa in the first years of the crisis, which began in 2011 and has developed into the worst since World War II.
SOS Mediterranee, founded in 2015, rescues hundreds of men, women and children each week from flimsy dinghies and boats in the Mediterranean, along with other NGOs.
Nicolini was recognised for "her boundless humanity and unwavering commitment to refugee crisis management and integration in response to the arrival of thousands of refugees on the shores of Lampedusa and elsewhere in Italy".
"I dedicate this prize to all those who did not make it across the sea because they were swallowed up, and also to Gabriele Del Grande," said Nicolini, referring to an Italian journalist arrested in Turkey this month while researching the lives of Syrian refugees.
"He was the first to count the Mediterranean's dead on a website, back when nobody even knew people were dying in the Mediterranean. He is now a prisoner in Turkey," she said, calling on the government to "bring him home".
The jury said SOS Mediterranee's Aquarius vessel, co-run by Doctors Without Borders, had saved more than 11,000 lives since it began search and rescue missions off Lampedusa in early 2016.
"We're so happy to be given this award together with Nicolini. We visited her when we were starting up and she said 'you are crazy but I am with you, because this is what we need after the failures of the EU'," said Sophie Beau, SOS Mediterranee co-founder.
The jury appealed to the international community "to ensure that the Mediterranean sea becomes, once again, a place where solidarity and intercultural dialogue hold sway, and that it ceases to serve as a watery grave".
Private rescue vessels sounded the alarm this weekend over the "unprecedented mass rescues" of people fleeing horrors in conflict-torn Libya, recovering seven bodies including that of an eight-year-old, and warning more migrants risked drowning without EU action.
Close to 37,000 people have been brought to safety in Italy so far this year, a 45 percent increase on the same period in 2016.
The EU's border control agency Frontex has accused donor-funded vessels of doing more harm than good by acting "like taxis" off Libya and tempting human traffickers to put as many people as possible out to sea in flimsy vessels.
Italian prosecutors have suggested they may have links with traffickers and in March named SOS Mediterranee's activity as being of interest to investigators, along with other private rescue vessels.
Their charges have been fiercely rejected by the NGOs, with SOS Mediterranee saying Wednesday it had "never, not once" been put in contact with migrants via smugglers.
"European governments need to show more solidarity to the humanitarian organisations that are working on the front line of this humanitarian crisis. Border control is not the solution," said Regina Catrambone, the director of MOAS rescue service.
UNESCO's Felix Houphouet-Boigny Peace Prize, created in 1989 to honour those making a significant contribution to peace, has gone in the past to Nelson Mandela, Israel's Shimon Peres and the late Palestinian leader Yasser Arafat, King Juan Carlos of Spain and former US president Jimmy Carter.