Police raided a home in Niddrie and found a "personal quantity" of the substance, which is now a Class B drug. A 26-year-old man is due to appear in court in relation to the incident.
A spokesman for Lothian and Borders police said: "We would urge anyone with information relating to drugs in their area to come forward.
"We would also like to remind people that mephedrone is now a banned substance and, if found in possession of it, you will be arrested."
After some high-profile incidents, the former "legal high" was swiftly outlawed.
Deputy chief constable Gordon Meldrum, director general of the Scottish Crime and Drug Enforcement Agency, added: "Future operations will be mounted to target those who continue to traffic the drug as well as those who are known to have stockpiled the drug ahead of the ban."