Bumrah had recently returned to the Indian team after recovering from an injury that saw him spending two months on the sidelines, but the speedster is now expected to be out of action for another four to six months.
"Bumrah is not going to play the World T20 for sure. He has a serious back condition. It's a stress fracture and he could be out for a period of six months," a senior BCCI official told PTI on conditions of anonymity.
It is understood that either Deepak Chahar or Mohammed Shami could replace Bumrah in the main squad. Both were named as stand-by players for the prestigious tournament by the BCCI.
Bumrah, who played two T20s against Australia, didn't travel with the team to Thiruvananthapuram for the series opener against South Africa on Wednesday.
The 28-year-old is the second senior star player to be ruled out after Ravindra Jadeja, who is recovering from a knee surgery.
"Losing Bumrah and Jadeja will be huge for India. We didn't expect that things will pan out as they have. He was rested for the Asia Cup precisely to manage his workload management. Now it remains a question if he was even fit enough to play the Australia series," the senior official told PTI.
Back stress fractures do not require surgery but a lot of time to heal.
Bumrah, who has a slinging action, puts a lot of pressure on his back during loading. Former West Indies pace bowling great Michael Holding had assessed that Bumrah was always a candidate for back injuries.