The draw, which was made by five-time Extra.ie FAI Senior Cup winner Gary Rogers on RTÉ 2FM's Game On, sees holders Dundalk travel to Finn Harps.
SSE Airtricity First Division side UCD welcome Waterford to the UCD Bowl, while St. Patrick's Athletic host Wexford FC.
Dates and kick-off times will be confirmed in due course with all matches set to take place in the week ending Sunday, September 19.
Extra.ie FAI Senior Cup Quarter-Final Draw
UCD v Waterford
St. Patrick's Athletic v Wexford
Finn Harps v Dundalk
Bohemian v Maynooth University Town
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Introduction:
Maynooth University Town travel to Dalymount Park to face Bohemians in the Extra.ie FAI Senior Cup quarter-finals.