The 28-year-old was out of action for eight months after rupturing a knee ligament while making his debut on loan at Yeovil Town in January.
Beaglehole has said that Bakayogo's latest problem, which he picked up in an Under-21s game against Fulham, could be another anterior cruciate ligament issue.
"I'm not a medical person but all the signs are there to say it's a similar injury to before," he told the Leicester Mercury.
"I'm really sorry for him, he is a real good lad. When he has dropped down with us he has always been part of the group and someone that puts everything in.
"I am really disappointed for him and I hope it's not a serious injury but the signs are not very good at this moment in time."
Bakayogo joined Leicester in July 2013.