Per Sam Smith at the team's official website, Richard Hamilton indeed tore a ligament in his foot during Saturday's game. It's not entirely clear if it was a partial or full tear, and Smith speculates (using sources or not, again...not sure) that it could only be a 1-2 week absence for Rip.
As explained there and here by KC Johnson, a tear is sometimes better than a severe case of (the common) plantar fasciitis, as it can be given a chance to outright heal instead of linger.
Given Rip's injury/recovery history, and the Bulls propensity for being lying liars, who really knows how long it'll be. All thing's considered, the SG is where the Bulls have a bit of depth, Marco Belinelli has picked things up a bit and Jimmy Butler is having a very fine season. But it's still not good news for a team needing all hands on deck most nights.