"He seems to think the time limit, at the very worst, will be around six weeks, but if it manages to knit itself together, he could be back in around three or four weeks," Bowen told the club's website.
He added that it was always better to be cautious in dealing with hand injuries for goalkeepers "... because the last thing you want to do is to put the problem at further risk.
"We will give it time ... and then Jack will strap it up and see how it feels - at this early stage we are loathed to put a definitive time scale on it."
Butland, who has started all 11 of Stoke's league games this season, could be replaced by Lee Grant for their next league game at Brighton and Hove Albion on Monday.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford)
