The raider, who is also believed to have been armed with a knife, went into the Broom Estate Post Office in Broom Place, Belle Isle, at around 6.20am on April 30.
He threatened a male member of staff before taking a cashbox and running off along Broom Place in the direction of Middleton Road.
Police are appealing for information and have released CCTV images of the incident.
Det Insp Sean Duggan, of Leeds District CID, said: “This was a very distressing incident for the member of staff involved to be confronted by a masked man brandishing a hammer at him.
“Although the man has his face covered, his clothing is distinctive and we would urgently like to hear from anyone who thinks they know who it might be.”
The man is described as being 5ft 10in to 6ft tall. of average build and aged under 30.
He was wearing a two-tone grey hooded top with darker sleeves, grey trousers and white and blue training shoes.
Anyone with information is asked to contact Detective Constable Tony Thompson at Elland Road Police Station via 101.
Or call Crimestoppers, anonymously and in confidence, on 0800 555 111.