Prosecutors in the lagoon city are investigating several people responsible for the MSC Opera, which suffered an engine failure before crashing into a tourist boat and a wharf on the Giudecca Canal on Sunday.
A number of port officials are also under investigation.
Four people suffered minor injuries in the incident, which has renewed calls for cruise ships to be banned from Venice.
MSC Cruises said it has begun repair work on the MSC Opera and has cancelled the remainder of the current cruise and offered passengers a full refund.
The liner itself remains docked at the Sant’Elena maritime station in Venice, where authorities are investigating the cause of the accident.
Passengers are allowed to remain on the ship while it stays docked in Venice until June 7, when the cruise was scheduled to end.
“All on board services and entertainment will continue to fully operate,” a spokesperson for MSC Cruises said.
“In addition, a free regular shuttle boat service to and from Piazza San Marco in Venice will be available to all passengers.
“For those passengers who prefer to leave the ship today or at any point and return home, MSC Cruises will provide all necessary assistance for the transportation and will take charge of any costs incurred.”