The line's Istanbul and Izmir stops are being replaced by alternatives in Greece, Italy and Malta.
The changes affect three of the line's ships: Costa neoClassica, Costa Pacifica and Costa Deliziosa.
A statement from Costa said: 'This decision will ensure the best experience for guests... The company is informing its guests and travel partners and has taken all measures to ensure minimum disruption in reaching and leaving the ship for those guests who have already booked their cruise."
The change of itinerary comes in the wake of a terrorist attack on the U.S. consulate in Istanbul by the Revolutionary People's Liberation Army Front (DHKP/C) earlier this month. Six people were killed in separate attacks on Turkish security forces, after a crackdown on terror groups such as the Islamic State and other militants.