Officers conducted a search at Tiki Tots in Nile Grove and found the class B drug growing in the building's loft space.
Police said parents had been completely unaware of the cannabis.
The cannabis was recovered by police on Tuesday. Officers said they were pursuing a positive line of inquiry.
Det Insp Paul Grainger, of Police Scotland, said: "This building was regularly occupied by young children and their parents who were completely unaware of the cannabis which was being grown within.
"Acting upon intelligence, we executed a search of the premises and made a sizeable drugs recovery.
"Our engagement with the public provides us with invaluable information and by working together we have ensured the safety of local parents and their children, as well as the wider community which these drugs were destined for."
Police in Edinburgh have recovered more than £64,000 worth of cannabis plants from a building which also houses a play centre for young children.