The robbery occurred in the Dalry area of the Scottish capital on Saturday night.
The green kit bag – emblazoned with the words Emergency Medical Response – contained drugs which could be dangerous if misused, according to Police Scotland.
The bag was stolen as ambulance staff attended to an incident on Caledonian Road at around 9.20pm.
Police Inspector Gill Lundberg said: “Stealing from emergency service workers trying to help someone is a despicable act.
“While the theft of this equipment has not impacted on the care of the patient, I am concerned what could happen if the stolen drugs were to be taken by a member of the public.
“These drugs can be dangerous if misused,” said Inspector Lundberg.
“I would appeal for anyone who witnessed the theft, or knows where these items are now, to contact police immediately.”
Police have not said which substances were inside the bag, revealing only there were “controlled drugs” that required medical training to administer.
Can you help us locate a medical bag which was stolen from ambulance staff earlier. Theft occurred about 9.20pm on Sat 17/11/2018 on Caledonian Road. Any info call 101 quoting incident 4228 of 17th November. https://t.co/ABCVbUfcmc pic.twitter.com/SgyLu1aI26— Edinburgh Police (@EdinburghPolice) November 18, 2018
Earlier this month, paramedics in north London had two iPads and a bag stolen from their ambulance while they were dealing with a “critical” emergency.
The thief took the devices and a bag containing personal items while staff were attending to a patient in Tottenham.
Anyone with information about the theft in Edinburgh is urged to contact Police Scotland on 101, quoting incident 4228 of 17 November.