The incident happened at around 8.10pm on Friday at the News Boys Newsagent in The Square.
An 80-year-old man was working within the shop when a man entered in possession of a Samurai-type sword and demanded money.
A struggle ensued between the suspect and the shopkeeper during which time a three-figure sum of cash was stolen and the victim sustained a minor injury to his hand.
Inquiries are ongoing and anyone who can help trace the man responsible is asked to come forward.
He is described as white, around 20-years-old and about 5ft 7ins tall.
Detective Inspector Paul Batten said: “This is an extremely unusual offence, given the style of weapon used and thankfully the shopkeeper was not seriously injured.
“We are treating this robbery with the utmost seriousness and I would ask anyone who remembers seeing any suspicious activity around the store on Friday evening to contact police immediately.
“Similarly, anyone who can help us identify and trace the male responsible is also urged to get in touch.”
Those with information can contact Dalkeith CID via 101 and quote incident number 3936 of October 6. Alternatively, an anonymous report can be made through the charity Crimestoppers on 0800 555 111.