Eurotunnel will be given six months to stop running services from the date of an order to that effect.
It could also find another owner for the MyFerryLink business, if that made MyFerryLink completely independent of Eurotunnel.
In reply Eurotunnel has said it will challenge the decision, and said it was 'astonished' that the company faces a ban from running the MyFerryLink ferries Berlioz and Rodin from the Port of Dover for 10 years.
Chairman and chief executive Jacques Gounon said: "The decision by the CMA is a denial of the reality of the situation. It penalises the consumer and puts 600 people out of work without any real justification."
MyFerryLink has said that the appeal process will not be determined until much later this year at the earliest, and has said it will continue to operate a full schedule throughout the summer season and beyond.