It has been learnt that Shami had suffered the injury during a training session after he returned from Australia, where the Indian team made a semifinal exit from the T20 World Cup.
Mohammed Siraj and Shardul Thakur have been named as backups and will travel to Australia shortly. The tournament will be held from October 16 to November 13.
"Deepak will take some time to get fit. So BCCI is sending three reinforcements; Mohammed Shami, Mohammed Siraj and Shardul Thakur," a BCCI official told PTI on conditions of anonymity.
The 32-year-old posted his negative report on his Instagram account, hours after the BCCI named veteran pacer Umesh Yadav as his replacement for the three-match T20I series against South Africa.
Veteran pacer Umesh Yadav, who played last of his seven T20Is in 2019 against Australia is back in the scheme of things, having recovered from a quadriceps injury.
India have picked Bhuvneshwar Kumar, Avesh Khan and Arshdeep Singh as the three specialist fast bowlers with all-rounder Hardik Pandya being the fourth pacer in the 15-member squad.
Although he has added a bit of it to his arsenal in recent years, with Shami, it was always about taking wickets. And his strike rate in Test cricket is a testament to that.
India's leading pacers reduce England's top-order for next to nothing, chase down 111 with all 10 wickets intact.
At the end of the day, India were 125/3, taking a massive lead of 257 runs. Cheteshwar Pujara was batting on a 139-ball 50 while Rishabh Pant was on 30 off 46 balls at the other end.
The 22-year-old Sunrisers Hyderabad pacer from Jammu produced one of the fieriest spells of fast bowling in the IPL history, snapping five wickets for 25 runs on Wednesday night.
Gujarat Titans skipper Hardik Pandya's outburst at team-mate and senior India bowler Mohammed Shami has not gone down well with the all-rounder's fans.
With five overs remaining, Gujarat Titans needed 68. The next 12 balls yielded three sixes and as many fours as Rahul Tewatia and David Miller couldn’t believe their luck.
IPL 2021 SWOT analysis: Pace concerns addressed but do Punjab Kings have same depth in spin department?
Punjab Kings finished sixth last season but missed out on a play-off spot narrowly after bouncing back strongly with five wins on the trot.
The in-form Indian pacer attributed his successful ODI comeback to his good Test performances over the last one year.
England now trail India by 18 runs with six wickets remaining in their first innings.
One of the greatest fast bowlers of all time and inarguably the best left-arm pacer to have played the game, Akram dissected the current Indian bowling attack.
Kohli's men will come into the series full of confidence after inflicting a 9-0 whitewash on Sri Lanka over three formats.
The selectors chose to rest leading spinners Ravichandran Ashwin and Ravindra Jadeja, as per the BCCI's rotation policy.
Asked to bowl, comeback man Mohammed Shami bagged four wickets as an under-fire India produced a disciplined bowling effort to restrict West Indies to a modest 205 for nine.
After a hectic six weeks of Indian Premier League, the two warm-up games will help the 'Men In Blue' get back into the 50-over groove.