Glasgow's other Cardiff casualty, Rory Lamont, will be out of rugby until at least next month.
Kenny injured his right ankle during the first half of the Cardiff match, and though he completed the game the damaged leg was in a support when he flew home with the squad on Saturday night. A subsequent examination revealed that the ankle had been sprained.
Rory damaged a hamstring in helping to prevent a Cardiff try on Saturday. He is receiving daily treatment, but it is too early yet to define precisely when he can return to full-time training.