The man we know as the USS Babineaux has been tough throughout his career, playing through the occasional dent in his mighty hull and still shelling quarterbacks. In fact, he's only missed three games over the last six season. But a partially torn anything is bad news, and this seems likely to at least slow Babs down over the next several weeks.
The Falcons aren't really in a position to lose him. Corey Peters is still dinged up and Babineaux is by far the best interior lineman the team has. Having him sidelined for any length of time would weaken the entire pass rush.
The good news is that he's one tough son of a Babineaux. It's unlikely Babs will let the injury sideline him for any significant length of time, and it's doubly unlikely he'll sit for the Eagles game. When Corey Peters is back and healthy, however, it might not be a bad idea for the big guy to take a game off to rest that up. Peria Jerry looked pretty good in the Bears game, all things considered.
So pray to your Football God of choice that Babs will both be okay and be able to play.