Bowe suffered the injury when he landed awkwardly following an attempted tackle by Northampton's Jamie Elliott late on in the round 4 fixture.
At this stage it is not possible to put a timescale on how long the Ireland winger's recovery period will be. A further update will be issued following the surgery, when the full extent of the injury will be known.
Bowe tweeted today: "Thanks to everyone for the messages. Will have surgery this week on my knee, it's not as bad as I feared so hopefully be back soon."
Ulster lock Dan Tuohy injured his calf during the game and will be assessed tomorrow morning, as will out-half Paddy Jackson who sustained a dead leg midway through the second half. An update on their fitness will be issued tomorrow afternoon.
The one-point loss in Belfast ended the province's 13-match winning streak this season, but Ulster still have a three-point buffer at the top of Pool 4 ahead of the final two rounds of matches.
Mark Anscombe's men wrap up the pool stages by entertaining Glasgow Warriors and then visiting Castres Olympique in round 6. Castres are second in the pool on 12 points, following a battling 10-8 home win over Glasgow this afternoon.
Speaking after his first competitive defeat as Ulster boss, Anscombe said: "It's sad because it's our first loss but we got beaten by a better team. We're still a good team and we'll bounce back.
"It happens and you've got to acknowledge it and respect it as Northampton did well and deserved their victory. We've got to go back and look at what we need to do better.
"Our execution was poor and we suffered from it. They got 10 points up in the first 18 minutes.
"We held them out well but I think we created enough opportunities to score points and we weren't patient enough and didn't have enough composure at crucial times.
"We tried to force it and they brought a little more passion than us to start with. Their physicality at the start got them going."
Ruan Pienaar missed a penalty from inside his own half and a second more kickable effort in the dying minutes, as the Ulstermen fought to overhaul the Saints in the second period.
A couple of promising counter attacks, one from a Pienaar charge down and the other from a trademark burst from replacement Paul Marshall, could have led to tries for the league leaders on another night.
But Anscombe remains confident that Ulster can return swiftly to winning ways and reach the knockout stages next month, adding: "Our destiny is still in our own hands.
"We're not relying on other teams to see how it goes, if we win our last two games we'll qualify. Not every team has that opportunity, we have and we need to take it."