Brown fractured the second metacarpal bone (between the wrist and fingers) in his left hand when he tackled for a 1-yard loss during the third quarter of the 27-10 victory at Detroit.
Brown likely will be fitted with a cast at some point, but the Dolphins didn't release information on his status other to say he would be evaluated on "an ongoing basis."
That's the same forecast for cornerback Michael Lehan, who also had surgery on Friday, but in his case to repair and stabilize a fracture in his nose.
If Brown can't play against Jacksonville, then Sammy Morris would start in his place, with Travis Minor serving as the backup.
Morris and Minor both had success against the Lions, but running the ball on Jacksonville will be a lot more challenging for the Dolphins -- particularly if Brown has to sit out the game.