The some 3,200 passengers and 1,023 crew on board the ship, the 290-metre-long Costa Concordia, were being evacuated by lifeboats, helicopters and other ships in the area, a statement from the Italian coastguard said.
They were being taken to the tiny island of Giglio and put up in schools, homes and churches for the night. The ship ran aground at about 10 p.m. (2100 GMT) near Giglio off the Tuscan coast.
The Italian news agency Ansa quoted rescue workers as saying at least six people were killed and a number injured, but that the cause of the deaths was not immediately known. Ansa said some people had jumped into the water.
No official confirmation of the reported deaths was immediately available.
About five hours after the incident, several hundred people were still on board the ship and waiting to be evacuated.
Ansa quoted passengers as saying the ship jolted as dinner was being served and that the electricity went out for a while before the evacuation operation began.
The Italian coastguard said the ship had taken on water and was listing about 20 degrees but that there was no danger of it sinking.
The cruise ship company said the cause of the incident was being investigated.
