The incident happened around 8.25pm yesterday when the bin was pushed from a bridge in the Torphin Road area onto the A720, Edinburgh City Bypass.
A car travelling westbound reported to have sustained minor damage when it struck the bin between the Dreghorn and Baberton junctions.
Those responsible are believed to have made off in the direction of Torphin.
Officers are now appealing for witnesses and asking anyone with information to come forward.
Sergeant Kieran Dougal from Oxgangs Police Station said: “Fortunately on this occasion no one was injured and the bin was quickly removed from the carriageway, however, this was an extremely reckless and dangerous act.
“I would remind people of the inherent dangers of throwing objects onto fast moving roads, especially from height and the potential catastrophic consequences this can have.
“I would ask anyone who witnessed any suspicious behaviour in the area on Sunday night, or who knows who is responsible, to contact officers as soon as possible.
“Equally anyone with information that can assist with our inquiries is asked to contact us immediately.”
Those with information can contact Oxgangs Police Station via 101, quoting incident number 3637 of 11 February. Alternatively a report can be made to Crimestoppers anonymously on 0800 555 111.