The 85-year-old died after the private refuse vehicle collided with her at 11.45am today.
The circumstances of the incident are not yet known.
A police spokesman said: “We received a report of a road traffic collision around 11.45am on Sunday 17 April.
“A refuse vehicle had been involved in a collision with an 85-year-old woman on Morningside Road, Edinburgh.
“Sadly the woman has passed away. A local diversion is currently in place at Comiston Road and Churchill Place.”
Buses are being diverted via Balcarres Street, Myreside Road, Colinton Road, Kilgraston Road, Blackford Avenue, Charterhall Road and Cluny Gardens.
Sergeant Andrew Miller, of the road policing unit, said: “We’re appealing to anyone who might’ve seen this elderly woman before the incident happened, or indeed the refuse truck.
“The woman was walking with a wheeled walking aid, similar to a Zimmer frame, and we’re hopeful anyone who might have seen her will come forward with relevant information.”
Morningside Road was closed for much of Sunday afternoon while police and ambulance crews remained on scene. Residents said complaints had previously been raised with councillors about the safety of junctions along the busy street.
Councillor Mark McInnes, who represents Morningside, insisted the council would look to see if any lessons could be learned.
He said his thoughts were with the woman’s family.