The Indian think tank wanted an experienced quick bowler at the death.
Shami's last T20 International was in the previous edition of the T20 World Cup held in the UAE.
Both Bumrah the BCCI should resist the temptation to make an early return to the game without completing the healing and rehabilitation process in full.
India are in dire need of an express pace bowler in Bumrah's absence. Bumrah was ruled out of the World Cup in Australia earlier this week due to a back injury.
Bumrah missing the showpiece event in Australia compounds India's problems in in the death overs.
Bumrah's absence will certainly affect India's chances in the marquee event in Australia as death bowling still remains a grey area.
Bumrah's spate of injuries, despite his workload being carefully looked after by the think-tank, has become a matter of debate.
The 28-year-old Siraj, a right-arm pacer, has so far played in five T20Is and picked up five wickets from them.
Who will partner Arshdeep Singh in the death overs is the big worry for the Indian team management.
Bumrah is the second senior star player to be ruled out after Ravindra Jadeja, who is recovering from a knee surgery.