The 31-year-old has had surgery, and he's not expected back in action until early May.
Wilson suffered the problem in the Magpies' dramatic 3-2 win away at Nottingham Forest last week.
He was forced off late in the match, with the ex-Bournemouth star seen using his shirt as a makeshift sling.
Speaking ahead of Newcastle's game against Bournemouth, Howe said: "It is no doubt a big blow for him.
"It's been a stop-start season for him. We hope he's back before the end of the season.
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"It was a strange injury. He got in a tussle with the centre-back at the end of the last match.
"We had it scanned and hoped initially he could continue, but when he went to see a specialist, I think it was apparent quite early that he needed it operating on."
It's a huge blow for the England international, who will now be in a race against time to get fit if he wishes to be included in Gareth Southgate's Euro 2024 squad.
Wilson started off the season in fine form having banged in seven Premier League goals in his opening nine matches.
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But he hasn't found the back of the net in the top-flight since October 28.
Newcastle are currently without a host of first-team players with matches against the Cherries, Arsenal and an FA Cup fifth round tie with Blackburn on the horizon.
Alexander Isak remains doubtful with a groin injury.
Though the same can't be said for midfielder Joelinton or goalkeeper Nick Pope, who remain out long-term.
However, Joe Willock, Jacob Murphy and Elliot Anderson could grace the pitch before March rolls around.
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Should Wilson fail to feature again this season, he may very well have played his last game for Newcastle.
He is tied down at St James' Park until 2025, with the player having no shortage of suitors.
talkSPORT revealed how Chelsea and West Ham were keen on Wilson in January, while he could have interest from Saudi Arabia in the summer.