The masked men, armed with what appeared to be a handgun, entered the Wellstone Rise Post Office at 8.55am on Tuesday.
They threatened staff and stole cash from the store, before leaving the scene in a car driven by a third man.
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There were no injuries but staff were left badly shaken.
Armed police were rushed to the scene and enquiries are still ongoing.
Police officers remain outside the store with post office staff, directing customers away from the store.
It is not yet known when the store will reopen.
In a statement, West Yorkshire Police said: "At 8.55am today (3/9) police were called to an armed robbery at Wellstone Rise Post Office, in Swinnow Lane, Leeds.
"Initial reports are that two masked man, armed with what appeared to be a handgun, had entered the shop and threatened staff before taking cash and leaving the scene in a car driven by a third man.
"No-one was injured but those involved were left badly shaken.
"Officers are currently at the scene and enquiries into the incident are ongoing."
Anyone who witnessed the incident or who has any information that could assist the investigation is asked to contact Leeds District CID via 101 quoting log number 342 of September 3 or call the independent charity Crimestoppers anonymously on 0800 555 111.