The incident happened at Hamilton and Inches jeweller in George Street at around 11.30am. Police said a number of men entered the jewellers.
Two police vans and an ambulance were stationed outside the store shortly afterwards.
By midday there were eight police vehicles and two ambulances.
One storekeeper said: "I only saw the ambulance and police arrive.
"It looks like it's another armed robbery. There has been a spate of them."
A Police Scotland spokesperson said: "Police responded to reports of a robbery at Hamilton and Inches on George Street where a number of men entered the premises armed with bladed weapons at around 11.30am today, before making off in a white BMW with a quantity of jewellery.
"Inquiries are continuing, and anyone who witnessed this is urged to contact police on 101."
One eye witness, who asked not to be named, said: "Three men came out of a BMW and ran into the shop. They were wearing masks and had a hammer, an axe and a machete.
"It was over in a minute or two.
"I don't think anyone was hurt. But they were shocked."
Police said they had recovered the white BMW abandoned in Edinburgh this afternoon but would not reveal the location.
Officers are hunting four people in total.