Rams Coach Steve Spagnuolo called it a "small fracture" that was shown to be non-displaced. Spagnuolo said Bulger won't wear a cast and instead will have the finger taped.
Spagnuolo said Bulger "won't do very much for two weeks, just to be on the safe side."
Kyle Boller will be the Rams' starting quarterback in Bulger's absence.
The Rams have a pre-season home game Friday against the Atlanta Falcons.