The robber struck on July 15 when he rushed into the Manor Estate Post Office in St Michael's Road, Aldershot, handed a bag over the counter and demanded the woman fill it with money.
But the quick-thinking employee triggered an alarm, forcing the thief to flee empty-handed. He made his getaway on a yellow bicycle and was seen heading towards the High Street.
Det Con Steve Mellish of Aldershot CID said the 42-year-old postal worker was very shaken by the experience.
"It must have been a very frightening incident for her. I saw her at the scene and because she was so shaken we could only get the bare facts," he said.
Det Con Mellish said the drama unfolded at 2.30pm when the woman was working in the post office section of the shop and her husband was working in the general store.
He said the suspect walked in and went over to the counter. "He produced a pistol-type handgun and pointed it directly at her at close range," said Det Con Mellish. "She was in an enclosed booth so there was only glass between them."
Despite the threat of force, the woman refused to hand over any cash and she frightened him off by pressing the panic alarm.
Det Con Mellish added: "Her husband heard the alarm and rushed round to the counter to see if she was alright. He then went to chase the offender but was stopped by his brother-in-law who warned him off because the man was armed."
He said they then spotted a police car and rushed over to report the incident. Police combed the area but there was no trace of the robber.
Det Con Mellish said the robber is aged 50, between 5ft 8in and 5ft 10in tall and slim, with dark, greying hair.
He was wearing a flat cap, dark sunglasses and a light blue shirt with a dark tank top over it.
A spokeswoman for the Post Office said: "Obviously we are concerned at this attempted robbery, as I would expect the sub-postmistress is upset at this incident, and we are fully sympathetic.
"We would appeal to anyone who may have seen anyone suspicious or running away from the post office to contact the local police.
"Any information which helps catch the culprit would be much appreciated."
Det Con Mellish urged anyone who saw anything suspicious at the time to call Aldershot police on 0845 0454545.