Pope, who was forced from the field in during his side's 1-0 win, has started every Premier League and Champions League game for Newcastle this season, but this injury will see him sidelined for the foreseeable future.
"He had a couple of appointments with specialists. [We're] still waiting for final news on what's going to happen," Howe told a news conference on Wednesday.
"We suspect he'll be operated on. Roughly out for four months but it's something we expected straight after the game."
ESPN reported on Monday that Spanish keeper David de Gea would be open to joining Newcastle. De Gea has been a free agent since his contract with Manchester United expired in July. However, Howe said Newcastle have not made any enquiries about replacing Pope.
"I've seen a lot of media headlines regarding goalkeepers and other players. We have not made any enquiries," Howe said.
"If we were to recruit now we'd be recruiting in every area on the pitch. It's a chance for the other keepers to consolidate their positions."
Pope's absence will see Martin Dúbravka get his chance. The Slovakian keeper replaced Pope for the final minutes of the game against Man United, and his only other appearance this season came against the same opposition in the League Cup.
"I've always had a high opinion of him. Martin is a high class goalkeeper, a brilliant shot-stopper and very good with his feet too so there's no hesitation about bringing him into the team," Howe said.
Newcastle completed back to back home league wins with victory against Man United, and Howe said he was even more impressed with that performance than the 4-1 win against Chelsea before that, or the draw with Paris Saint-Germain in between.
"It has been a big effort from the group, the players have really grasped the situation we are in, they have really stood up," he said.
"We took a lot of confidence from the Chelsea game, which was a massive result for us.
"That led to Paris which was a difficult one to talk about and then what a response against Manchester United. I thought that was our best performance of the season."
Howe's side travel to face Everton on Thursday, and while Newcastle's home record is impressive with seven wins from eight, away from home they have just one win from six, and suffered three defeats.
"They [Everton] are a very strong, physical team. They will pose questions for us defensively which we will have to answer, we are going to have to respond to those questions," Howe said.
"It is a big game for us. We know our away form has to improve."
Newcastle are sixth on the Premier League table on 26 points, 10 points off leaders Arsenal, while Everton are third from bottom on seven points after their 10 point deduction for breaching financial sustainability rules.