"The 98 people of different African nationalities set off from the Libyan coast in an inflatable boat... Probably for the (Italian) island of Lampedusa," spokesman Taoufik Rahmouni told AFP.
"The navy was alerted by a distress signal, and when it got there the boat was empty. The migrants had taken refuge on a small dock near the platform of the Ashtart oil rig" off the southern island of Djerba.
Women and children were among them, Rahmouni said, including the Congolese boy, who was evacuated to hospital by helicopter.
Tunisia and Libya have seen a rise in the number of African migrants attempting the perilous journey to southern Europe by sea, often in overcrowded, unseaworthy boats.
Up to 600 migrants -- mostly from Eritrea and Syria -- drowned in two shipwrecks last October off Lampedusa. Italy's southernmost territory, it lies some 250 kilometres (155 miles) from Djerba.