British tech entrepreneur Mike Lynch is reportedly among those missing.
There were 22 people on board in total – 15 people were rescued including a one-year-old child.
The captain of a nearby ship says he found15 survivors in a life raft and alerted the coastguard.
One English woman tells an Italian newspaper she held her daughter “with all her strength” to stop her drowning.
The 56m (183ft) yacht, the Bayesian, was flying a British flag, and was around 700 metres from the harbour when it sank.
The yacht is owned by Revtom, a firm registered in the Isle of Man.
In the company’s latest annual statement, filed in April, Revtom’s legal owner is named as Angela Bacares, Lynch’s wife.
