"The ship is turning around and heading approximately 20 nautical miles east to bring it nearer to the coast and within reach of a helicopter," cruise line Fred. Olsen said in a statement.
The crew of the MS Balmoral, which is hosting the memorial cruise, is working with the Irish coast guard to assist a passenger who became ill.
iReporter Tom Byron, who is on board the Balmoral, told CNN the ship made an hours-long "huge U-turn in the ocean" to get closer to shore for the airlift. The cruise line has not provided details of the emergency situation.
The ship set sail from Southampton, England, on Sunday and stopped at the Titanic's last port of call in Cobh, Ireland, on Monday. The "sea was a little rough" after departing Cobh, according to the cruise line's Facebook page.
Byron said many passengers are seasick as a result of rough seas and 20-foot waves. "Shows canceled for the day due to lots of rocking and bumping," Byron said in an e-mail.
The cruise itinerary includes a memorial service in the spot where the Titanic sank 100 years ago on Sunday before heading to Halifax, Nova Scotia and New York, the ship's final destination.
The ship will resume its journey as soon as the passenger is evacuated for treatment, and the timing should not be affected, the cruise line said.