Shah claimed five wickets in the first match of the series, which England won by 74 runs, but missed the second match as the tour side triumphed by 26 runs to seal a 2-0 win in the series before the final showdown on Saturday began.
Shah will now travel to Lahore for further assessment at the National High Performance Center before commencing rehabilitation.
“The team leadership has not asked for his replacement at this stage,” the PCB said in a statement. “Tomorrow afternoon, both Pakistani and English teams will travel to Karachi.”
Pakistan is also without injured pacemakers Shaheen Afridi and Haris Rauf.