The strikes erupted last week as employees fight to disrupt the company's plans to cut costs by reducing salaries and the number of crossings.
About 8,000 passengers have been affected, the company said.
"Given the strikes that have been been launched in an ill-timed manner, without warning, and the possibility they will be renewed, Brittany Ferries management can no longer ensure the operations of its ships and services to passengers under normal conditions," the company said in a statement.
The company said it had decided to "stop all ships until further notice and disembark all crews with the exception of security personnel."
Among the ferries cancelled on Friday were routes from Plymouth and Portsmouth in Britain to Roscoff, Caen, Cherbourg and Saint-Malo in France and to Bilbao in Spain. Routes were also cancelled between the Irish city of Cork and Roscoff.
The company carries 2.6 million passengers per year, 85% of them British.