The Cameroon forward limped out of Wednesday’s defeat at Brighton late in the first half, having opened the scoring from the penalty spot.
That was the 24-year-old’s seventh Premier League goal of the season and his overall tally of goal contributions stands at 11 in 15 League games.
"It is bad," Frank revealed ahead of Saturday’s trip to Sheffield United. "He’ll have a scan later, but we don’t know the exact number of weeks he will be out.
"He will definitely not play on Saturday [against Sheffield United], and he will be out for weeks. We will know more in the next couple of days."
The prospect of playing without him will be of major concern to Frank, who is already missing star striker Ivan Toney.
Mbeumo, alongside Yoane Wissa, has stepped up to score the goals required while the England international serves his ban for breaching betting rules.
Frank is missing a raft of other key players too with record signing Nathan Collins ruled out alongside Rico Henry, Aaron Hickey, Kevin Schade, Kristoffer Ajer, Mathias Jensen and Josh Dasilva.