The Hoops have been drawn against last season's beaten finalists, while Bohemians host financially-stricken Dundalk in the FAI Cup quarter finals
Shels were beaten in the final of the competition last year and the Airtricity Premier Division champions will take on their Dublin rivals with a view to winning their first FAI Cup since 1987.
Speaking to the Irish Times after the draw, Shelbourne boss Alan Mathews said that the game should be a 'great occasion'.
He said: “There’s a great cup tradition between the two clubs and it’s probably the tie of the round.
“Certainly to have a club like Rovers coming to us for a game like this is terrific; we’ll look forward it and I know the lads will be determined to make it a great night for our fans.”
Elsewhere, Liam Buckley's St Patrick’s Athletic will host high-flying Drogheda United at Richmond Park, while Bohemians will play Dundalk in a third all-Premier Division tie.
Derry City, meanwhile, will play the winners Waterford United and Mervue United tie, which has been postponed twice already.
The FAI Cup quarter final matches will be played on the weekend of September 16.
FAI Cup Quarter Final draw
Shelbourne v Shamrock Rovers
Bohemians v Dundalk
St Patrick’s Athletic v Drogheda United
Derry City v Waterford United/Mervue United