A Pakistan Cricket Board official confirmed that Shah sustained the injury during the one-day practice match against the Bangladesh Board Presidents XI on Wednesday.
He said Yasir had injured his left hand while fielding and required three stitches on his left thumb but for the time being he will remain with the touring squad to see if he can recover in time for the two-Test series.
Babar, 36, was already named for the two Test matches and chief selector Haroon Rasheed said his selection was logical given his experience and form.
Pakistan also lost fast bowler, Sohail Khan due to a back injury, prior to the team's departure for Bangladesh last week. He was replaced by left arm pacer, Junaid Khan who took four wickets in the practice tour match on Wednesday.
