The pair entered the Maysum takeaway on Craigentinny Road at 23:00 on Friday, with the man approaching the counter and demanding money.
After staff refused, the pair fled the scene and were last seen heading eastwards down Craigentinny Road.
The man was in his 20s, 5ft 7in (1.7m) tall and was wearing a cream-coloured jacket with the hood up and a scarf.
The woman was about 5ft 9in (1.75m) tall, and wore a black hooded jacket, a pink hat, dark trousers and a white scarf over her face.
Police are carrying out door-to-door inquiries and reviewing CCTV footage, and have appealed for anyone who may have seen the suspects to come forward.
Police are looking for a man and a woman who tried to hold up a Chinese takeaway in Edinburgh on Christmas Day.