The Welsh defender started at right-back in the Capital club's opening game of the Ladbrokes Premiership season, but was forced off through injury after a heavy challenge from Buddies winger Ilkay Durmus.
The former Yeovil Town full-back received treatment from Easter Road physio Nathan Ring and attempted to play on, but was replaced by Sean Mackie shortly before half-time.
Reports on Wednesday morning indicated that the injury was not as bad as first feared and the 23-year-old could be fit for Sunday's trip to Ibrox. However, the club have revealed that James will miss Hibs' next few games as a result of the injury.
Speaking to the club's official website, head coach Paul Heckingbottom said: "It’s a shame for Tom because he’s settled in well since signing in the summer and worked had to earn a starting slot in that first league game against St Mirren.
“We hope he responds well to treatment and we won’t be without him for too long. In the meantime, it gives someone else an opportunity to stake their claim.”
Heckingbottom earlier this week questioned some of the decision-making by the referee and his assistants during Saturday's match, and branded the challenge on James "shocking".
Speaking after the match he added: "[Durmus] is nowhere near the ball and it's high on Tom's calf.
"He's pulled him over on his ankle and he's turned his ankle so we'll have to have a look. The tackle is horrific."
Heckingbottom will have been relieved, however, to see Ryan Porteous and Vykintas Slivka come through 90 minutes unscathed as the pair lined up against Elgin City in the Tunnock's Caramel Wafer Challenge Cup at Easter Road last night.
Porteous, 19, is working his way back from a knee injury that has kept him sidelined since January, while Lithuanian midfielder Slivka has only just overcome a hip injury sustained on international duty.The Scotland Under-21 cap scored the opening goal last night with a trademark bullet header, and the two sides swapped the lead back and forth as Heckingbottom and No.2 Robbie Stockdale watched Lee Makel's development side run their League Two counterparts close, with just Matthew Cooper's injury-time winner separating the sides in the end.