Two men scaled the perimeter fence of the DHL depot in Caputthall Road around 9.15pm, before one of them broke into the warehouse.
He then stole a quantity of cigarettes from a pallet, before being chased from the depot by staff.
The pair were last seen getting into a dark grey coloured people carrier, possibly a Toyota, that was driven by a third man.
The two suspects are both described as white, around 6ft tall, and medium build.
The main suspect is described as being in his mid-40s, with a Glasgow accent, and wearing a full-face balaclava, dark coloured hooded top with the hood up, a high-visibility vest, stonewash jeans, and white trainers.
The other man is also described as being in his 40s, and wearing dark clothing. He wore a black Tammie hat or rolled-up balaclava on his head. There is no description available of the driver.
A Lothian and Borders Police spokesman said: “The main suspect was undeterred by the presence of staff within the warehouse, and may have made off with a larger haul had it not been for the intervention of staff who gave chase.
“The value of the stolen cigarettes is estimated at several thousand pounds, and we are appealing to anyone who has information that can lead us to the suspects.
“We are particularly interested in speaking to anyone who recalls seeing the getaway vehicle – a dark grey people carrier – in the area of Caputthall Road on Friday night.
“Anyone else who noticed any suspicious activity in the area at the time, or who has any other information that can assist our inquiries, should also get in touch.”
Anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.
