The Impact Player rule allows teams to substitute one player.
India and Pakistan will square off in Dubai on Saturday.
Bumrah's participation in the Afghanistan T20I series is subject to fitness clearance.
The three T20Is are scheduled to take place between September 13 and September 17 in Delhi.
PCB sacked 7 players and 2 coaches immediately after losing the first two Tests in England.
Shubman Gill and Virat Kohli will play for India against West Indies in 3-ODI series in late September.