The 32-year-old fifth in line to Britain's throne bought last-minute tickets to 'The Curious Incident of the Dog in the Night-Time' at Gielgud Theatre in the West End theatre district of London, according to UK media reports.
"As an actress Meghan loves the theatre so this was an obvious date to go on," a friend told 'The Sun'.
Earlier this week, the couple were spotted buying a six-foot Christmas tree together and seen walking hand in hand.
"They came in to buy a tree, they were looking at trees and I went over to help them pick the tree," said Zaqia Crawford, from the Pine and Needles store in London's Battersea Park area.
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Markle, star of the hit US television series 'Suits', flew in to the UK from her Toronto home early on Monday.
Prince Harry lives at Nottingham Cottage in Kensington Palace, next door to brother Prince William and sister-in-law Kate.
He is expected to spend Christmas at his grandmother Queen Elizabeth II's estate in Sandringham, but Markle is unlikely to be joining him, as royal convention means partners are only invited to join the festivities once they are engaged to a family member.