The pre-planned operation was launched at Duddingston Row shortly before 11am.
A police source said officer executed a warrant but there was no connection to the killing of Bradley Welsh.
One resident posted on Twitter: “A typical Easter Friday morning with Duddingston Row closed by the armed response unit and yours truly being asked to move on.”
Mr Welsh, 48, was gunned down outside his home in Chester Street on Wednesday night.
A Police Scotland spokesman said: "Police in Edinburgh, supported by specialist resources, carried out a planned operation at an address in Duddingston Row on Friday 19th April.
"Inquiries in relation to this matter are ongoing."