"He's going to be out for at least four-to-six weeks if it's a regulation break," said head coach Rob Baxter.
"If it's anything worse than that then, that time lengthens.
"Injuries happen in rugby and you've just got to get on with it.
"Obviously you want all your players fit, and Sireli's a great player, I'm not going to run away from that, but one man doesn't make a team. We've just got to move on."
Baxter will hope to have the 31-year-old available for his side's back-to-back games against Newport Gwent Dragons in Rounds 3 and 4 in December.