The Tunisian vessel had been attempting to steal the engine of the refugee boat carrying 34 people near the island of Lampedusa. During a scuffle, the girl fell off the boat and has been missing since.
The boat, which had departed from the Tunisian coastal town of Sfax, was later picked up by the Italian coast guard and Guardia di Finanza, the police department which handles crimes related to smuggling.
The rescued people were taken to Lampedusa. When refugees arrive on the Mediterranean island, they are taken to a reception camp, which has capacity for around 400 people, but currently houses around 2000.
Lampedusa is located between Sicily and North Africa, around 190 kilometres from Sfax. Thousands of people drown every year trying to cross the dangerous route to Europe, which is controlled by illegal smugglers.
Italy's new right-wing government has made conditions for refugees attempting to reach Italy even more complicated. At the same time, the number of refugees arriving in Italy is rapidly increasing, according to the Interior Ministry.
AAP