Police were called to the East Neighbourhood Centre on Niddrie Mains Road at around 11.30am after council staff raised the alarm.
Officers searched the venue as a precaution however it is believed that the threat was a hoax.
A Police Scotland spokeswoman said: “Police in Edinburgh were called to an address on Niddrie Mains Road at around 11.20am this morning following reports of a suspicious phone call.
“In line with their standard procedure, staff were evacuated and officers searched the premises.
“There has been found to be no danger to staff or the public and enquiries are ongoing.”
The centre houses a range of council services, a community space, and Craigmillar Library.