The raid on the St Giles News Plus shop - in the St Giles Terrace area - took place at about 07:45.
A man brandishing a weapon demanded money from a shop assistant but fled empty-handed.
Police believe the man may have been in the vicinity of the Co-op on St Boswells Terrace a short time before the alleged incident.
The suspect is described as white, mid-20s in age, approximately 5'9" in height, slim build, wearing a large black jacket, dark coloured dress trousers and dark dress shoes. The man had a local Dundee accent.
Police in Dundee are investigating an attempted armed robbery at a local shop.