The cup clash was originally scheduled for Saturday November 17, but the League of Ireland Premier Division ends nearly a month earlier, in late October.
Bohs have three league games remaining; away to Sligo Rovers and Bray Wanderers before hosting Dundalk on the final day of the season on October 26 - more than three weeks before the quarter-final was due to be played.
Alternative dates for the match have been considered but the SPFL has confirmed that “none have been found to be satisfactory”.
Instead, the fixture is likely to be delayed until the new year, with the league suggesting “early 2019”.
The Irish season is likely to start up again in late February, shortly after the cup semi-finals are due to take place.
A statement from the SPFL read: “We will work with both clubs and our colleagues at the League of Ireland to find a suitable date, likely in early 2019, and will announce details in due course.”
The tournament is not without its detractors; earlier this year Dunfermline manager Allan Johnston and winger Kallum Higginbotham questioned the tournament’s make-up when they were drawn to face London-based side Boreham Wood in the second round.
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Johnston said: “I still don’t understand why these teams are in our competition in the first place. I don’t understand why they come in in later rounds. Surely if they are going to take part in the tournament they should come in in the first round? It’s a Scottish competition. I think it should be for Scottish clubs.”
Higginbotham admitted that the competition wasn’t a top priority, adding: “I don’t know where else you would find opposition from different leagues in a [domestic] cup competition.
“I just can’t get my head round that. We need to go down there and play the game but it’s not ideal. I wouldn’t say teams are disregarding the competition, but it is definitely not high on the priority list.”
Former Livingston boss David Hopkin branded the competition “beyond silliness”, highlighting the logistical problems for part-time Highland League teams in facing teams from other countries.
The Bradford manager said: “It’s beyond silliness now. It used to be a cup for the lower league teams, with a chance of winning some silverware.
“Now you’ve got to travel to Boreham Wood and Ireland and other places. It should be a Scottish cup competition but you could end up with a Welsh, Irish or English team winning it.
“If you’re a part-time Highland League team and have got to travel to Wales and Ireland to play in a game, you’ve got to take the time off work. You get drawn away to somewhere ‘abroad’ and players will have to take two days off.
“You might have some of the expenses covered but not enough. It just becomes a hindrance. I can’t see why it still can’t be just the Scottish clubs.”