The 19-year-old suffered the injury during Tuesday's 5-1 home loss to Charlton Athletic in League One.
The Chelsea loanee, who has made six league starts for Rovers so far this term, was taken to hospital after the game for treatment.
"A bad night got terribly worse," boss Darrell Clarke told BBC Radio Bristol.
"It looks like a fractured arm. It's very disappointing, especially with James Clarke out as well, so we have a couple of centre-halves missing."
Bristol Rovers defender Jake Clarke-Salter is set to be out for between eight and 12 weeks after fracturing and dislocating his elbow.