Scans have revealed that the centre-half damaged ligaments in his left ankle during the game against Millwall.
Roberts came down heavily, rolling the joint, after an aerial challenge and had to be taken off on a stretcher in the 26th minute of the 1-1 draw.
The news is a blow to both player and the side as Roberts has been in the best form his Blues career this season.
But Pep Clotet admitted it could have been worse.
"It is not as bad as it could have been," said the Head Coach. "He is a strong structured, big player. A lot of weight came down on his ankle and could have broken his ligaments.
"Fortunately, it is mid-term absence. Nothing below four to six weeks.'
Harlee Dean came on for Roberts as substitute as Jake Clarke-Salter kept his place in the heart of defence, despite the Captain being free from suspension.
Geraldo Bajrami has been added to the recent First Team squads as extra defensive cover and will continue to be on standby.
Blues have Wes Harding who can step in should anything happen to Dean or Clarke-Salter, who scored the equaliser against Millwall in a commanding display.
Midfielder Gary Gardner, meanwhile, could be in line for a Blues Under-23s appearance to aid his recovery from a knee injury.
Gardner has been back in full training for a couple of weeks and Clotet said: "For his confidence and for himself to get his fitness back in shape, he could play a 23s game."
Blues Under-23s next match is on Friday against Nottingham Forest at Alfreton (7pm).