The Belgium international had to be replaced in the 5-0 defeat to Manchester City on Saturday afternoon with a quarter of the game left to play after complaining of a knee injury.
Hodgson fears that Benteke is facing a spell on the sidelines while he recovers, ruling him out of next week's trip to Manchester United as a result, but the former England chief is remaining hopeful that it is only minor damage.
"He's not well - we think it's a form of ligament damage and I don't know quite how bad that ligament damage is," he told reporters. "He's going to have a scan on Sunday. It will mean he won't be playing in the next game, which we could do without at this moment in time."