Published: 2017-08-29 21:40:04 BdST
The 26-year-old went wicketless in the current first Test at the Shere Bangla National Stadium and was into his second over on Tuesday when he sustained the injury and walked off of the ground.
Hazlewood's injury leaves Australia with three of their pacemen sidelined less than three months before the Ashes series against England.
"He's going to be really hard to replace. He's played all but one of the last 30 Tests," pace colleague Pat Cummins told reporters after the third day's play.
"He said it is going to be pretty hard sitting at home watching. He hasn't done that for three or four years. So he's a big member around the group.
"I am going to miss having dinner with him every night, but we have got Jackson Bird waiting in the wings, which is great."
With Australia needing 156 more runs to win with eight wickets in hand, Hazlewood will be available to bat, and Cricket Australia is likely to name a replacement on Wednesday.
Chittagong hosts the second Test from Sept. 4, while Australia play five one-dayers and three Twenty20 Internationals in India, starting on Sept. 17.
Hazlewood's injury is a fresh concern for Australia who are also waiting for quicks Mitchell Starc (foot) and James Pattinson (back) to recover ahead of the Ashes series, which begins on Nov. 23.