The wing damaged knee ligaments while playing against Northampton in December, and he has revealed to UTV Sport that he will not be back to face Saracens on 6 April at Twickenham Stadium.
The 28-year-old underwent surgery in the days following his injury and while his recovery time was expected to be significant, some had hoped he would make an appearance sooner than predicted.
However Bowe, who also missed out on the 6 Nations this year, has now revealed he will not be part of Mark Anscombe's line-up despite not having a firm date for his return to Ulster.
"Probably middle to late April," he explained. "I would love to be back for the quarter-final but it might be a little bit too early.
"I think that it is a tough time to be injured and watching the 6 Nations and Ulster going so well, but it is just a case of trying to stay patient and positive and get myself back as fit as I can."
Ulster made it to the final of the Heineken Cup last year at Twickenham, but were beaten to the title by Leinster.
They are hoping to avenge the pain of that experience by going one better this season.
"To go to a team like Saracens will be very difficult opposition, but I think our away form this year has been superb, so I think we will go over there confident.
"We will hopefully have a great fan base, a lot of white shirts over there singing 'Stand Up For The Ulster Men' and it really rings around the stadium," he said.