After visiting a bar, the couple returned to their cabin but the door key did not work and Mr Cowley went to a reception area to resolve the problem, leaving his wife sitting outside the cabin.
The police statement said: "CCTV and witness accounts show Mrs Cowley go alone to a sun lounge on the ship shortly after 1am on Friday.
"Searches of the ship failed to locate Mrs Cowley, who has since been reported missing."
Mrs Cowley is described as white, of medium build, around 5ft 4ins. She has black bobbed hair with red highlights. She was last seen wearing a grey jumper, black leggings and black boots and has several distinctive tattoos, including the words "Mrs Cowley" written on her forearm.