The Lilywhites will travel to Tallaght Stadium in the last eight, while Drogheda United host Derry City at United Park
Lilywhites boss Stephen Kenny will come head-to-head with his former employers at Tallaght Stadium on the weekend of Sunday, September 14, with the duo set to meet in the EA Sports Cup final at Oriel Park the following Saturday, September 20.
Drogheda United have been paired against Derry City after overcoming non-league side Malahide United in the third round, while Avondale United or St Michael's will play host to Finn Harps.
The quarter-final will also feature a Dublin derby as either Shelbourne or St Patrick's Athletic have been drawn against Bohemians. Shels and the Saints are forced to replay at Tolka Park after Friday's clash at Richmond Park ended in a 1-1 draw.
FAI Ford Cup quarter-final draw:
Shelbourne/St Patrick's Athletic v Bohemians
Drogheda United v Derry City
Shamrock Rovers v Dundalk
Avondale United/St Michael's v Finn Harps