The group had halted its missions with its Aquarius ship in December 2018 after they said it was blocked by some EU governments following nearly three years of operations and the rescue of 30,000 migrants at sea.
Libya, caught up in civil conflict since the 2011 uprising killed dictator Moamer Kadhafi, remains a major and dangerous transit route for mostly sub-Saharan migrants trying to cross the Mediterranean to reach Europe.
EU states disagree on how to handle the migrants and some are taking a more hardline position, turning away rescue ships as they seek to dock to drop off rescued migrants.
The Ocean Viking, the successor to the Aquarius, left Marseille at 2000 GMT, according to an AFP journalist aboard the vessel.
The Ocean Viking, displaying the red and white colours of its new Norwegian flag, is expected to reach the central Mediterranean in two to three days.
“A lot of (migrant) crossings are taking place right now, that's related to the summer weather conditions but also to the situation in Libya, which has become a real trigger and explains why people are taking even more risks than before,” Frederic Penard, the rescue group's operational director, said.
Funded in partnership with Doctors Without Borders (MSF), the Ocean Viking has 31 people onboard to deal with rescue operations, including crew, maritime rescuers, doctors, a midwife and a cultural mediator.
The UN migrant agency (IOM) says at least 840 people have gone missing so far this year trying to cross from Libya's coast to reach Europe, most of them in the central Mediterranean.
The Ocean Viking will not enter into Libyan waters, the rescue group said.
Civil society rescue operators say they face increasingly hostile reactions from some EU states which are resisting taking in rescued migrants. Only a few civilian rescue vessels are still operating in the Mediterranean.
Italy's far-right Interior Minister Matteo Salvini has banned some rescue ships from entering Italian waters.
On Friday, at least 164 migrants rescued by Spanish and German NGOs were stranded at sea unable to enter Italian ports. The German ship was allowed to dock in Malta with 40 migrants on Sunday.