The 22-year-old went down in the first half of the match at Ibrox after colliding with pitchside boards, and left the stadium in a boot and knee brace.
His injury came hours after it was revealed Rangers had rejected a big-money bid for the player from Galatasaray.
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Chermiti, capped at U21 level by Portugal, joined from Everton last summer in a deal worth up to £10m and scored 15 goals and provided five assists across all competitions last season.
That has led Ibrox chiefs to value him higher than the club-record fee they received for Calvin Bassey, who joined Ajax for an initial £19.6m in 2023.
Speaking after Sunday's defeat to Hibernian, which left McInnes winless in his first three games as Rangers boss, he said: "Disappointed for the big fella that he has to come off on a stretcher. I thought he was looking bright and running gaps.
"He played with a bit of purpose and there's no doubt we missed that, but he's left in a boot and his knee in a brace.
"It's no surprise that he's a player who's got a big tag on him and he's got high potential, but thankfully he's our player and that will continue to be the case."
Rangers close in on Driouech
Rangers have made nine signings this summer, and that number is set to rise this week.
A £6.5m deal has been agreed to sign winger Couhaib Driouech from PSV Eindhoven, who is completing his medical and paperwork ahead of moving to Ibrox.
Burnley and Celta Vigo had also shown interest in Driouech - who has scored 12 goals in 61 games for PSV, including three in the Champions League last season, plus provided 10 assists.
Born in Holland, he has also played for Heerenveen and Excelsior, plus been capped by Morocco at U23 level.
At the club's shareholder meeting on Monday, chairman Andrew Cavenagh revealed the club are looking to add between three and five more players this summer.
It is understood the backline is among areas expected to be strengthened before Scotland's 5pm deadline on September 3.
Aston Villa right-back Kosta Nedeljkovic is a possible target after initial talks, while Rangers are also considering Hugo Siquet of Club Brugge.
There have also been discussions over a move for former Hearts left-back James Penrice, who is at Greek side AEK.
Meanwhile, Mohamed Diomande is expected to be the next outgoing, with Turkish club Corum FK set to sign the midfielder for around £4.5m.
