Sources told ESPN.com that the hand injury -- unrelated to the torn quadriceps muscle that has sidelined Griffin since Dec. 26 -- is expected to keep him out "a matter of weeks, as opposed to days."
Sources close to the situation said late Monday that the Clippers are still evaluating the severity of the new injury but are expected to provide an update Tuesday.
The Clippers have gone 11-3 since Griffin was lost to the quadriceps injury, but only two of those wins have come against teams with records of .500 or better.
L.A. plays at Indiana on Tuesday and at Atlanta on Wednesday before returning home to square off with the Lakers on Friday at Staples Center.
Griffin originally hoped to return to the lineup during this road trip.
Report: Griffin likely out 'weeks' with suspected hand injury
Marc Stein reports the latest on Blake Griffin, who is expected to miss an extended amount of time with a suspected hand injury.