Bowe was carried off late in the second half at Ravenhill after a lengthy stoppage.
In a statement Ulster said: "An initial scan this morning revealed that he has sustained significant lateral ligament damage to his right knee.
"He will undergo surgery later this week to repair the damage.
"At this stage, it is not possible to put a timescale on how long his recovery period will be."
Ireland kick off this season's Six Nations tournament against defending champion Wales on February 2.
Bowe, whose prospects of touring Australia with the British and Irish Lions could conceivably be jeopardised by his current injury, is an integral part of Ireland coach Declan Kidney's plans.
Ulster continue to make the running in Pool 4 on 15 points but their shock 10-9 defeat to Northampton has cast a shadow over their Heineken Cup campaign.
After gaining a winning bonus point in Franklin Gardens eight days earlier Ulster were expected to win comfortably but that wasn't how things transpired.
In a low scoring, scrappy game, Steve Myler gave Northampton an early lead before the only try of the game came when GJ van Velze completed a fine, flowing move by shrugging off the challenge of Andrew Trimble and going over.
Myler's conversion made it 10-0 to the Saints but Ulster fought back with two Paddy Jackson penalties before half-time and another Jackson penalty three minutes into the second half, left just a point in it.