The man, who had his head and face covered with a short black scarf, took a small amount of money from a staff member in the Elgin Food Market, in Elgin Rd, Mornington, just after 6pm, Senior Sergeant Brian Benn said.
The man then left the premises.
No-one was injured in the incident.
A large knife and a purple and black jacket were discovered, discarded, several streets away.
Police canvassed the area seeking witnesses and Sergeant Dave Scott urged anyone who saw anything suspicious to contact Dunedin police.
Police were keeping an open mind over whether there were any links with Sunday night's robbery at a Halfway Bush dairy, he said.
In that incident, a masked man entered the On the Spot Halfway Bush Convenience store and pulled a gun on the shopkeeper, demanding the legal high Kronic.
The offender has not yet been located.
