Zazai will be replaced by travelling reserve Gulbadin Naib (31) in Afghanistan's 15-player squad for the tournament in Australia.
Afghanistan are bottom of Group 1 with two points from three matches in the Super 12 stage.
They lost to England and their games against New Zealand and Ireland were abandoned due to rain.
Afghanistan need to beat Sri Lanka on Tuesday and Australia on Friday to have any chance of qualifying for the semi-finals.