The highly rated Bosnia Herzegovina international, who has been linked with a number of big clubs, suffered the injury in training on Christmas Day.
Begovic was therefore absent from the Stoke team to face Newcastle United on Thursday, with former Sunderland shot-stopper Thomas Sorensen taking over.
Youngster Jack Butland was recalled from his loan spell at Championship outfit Barnsley to take a place on the bench at St James’ Park.
"A ball struck Asmir on the end a finger in the closing stages of training yesterday (Wednesday)," revealed Stoke manager Mark Hughes prior to the Newcastle fixture.
"It's a blow but we've got great back-up in Thomas Sorensen and Jack Butland, who we've recalled from his loan with Barnsley."
A reliable presence between the posts for Stoke, Begovic has not missed a Premier League game since the last day of the 2011-12 season.
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
Alexander Isak puts uncertainty over his Newcastle United future to bed amid fresh PSG and Arsenal links
