The 31-year-old, who scripted history by becoming first Pakistan batsman to score double century in Australia in the Boxing Day Test, sustained the injury when he was on 12 during the opening ODI at the Gabba before returning later in the innings.
In Azhar's absence, Mohammad Hafeez, who has captained the country in Test and T20 cricket, will lead the side in the upcoming ODI and probably the third game in Perth on January 19.
While confirming the news, the Pakistan Cricket Board (PCB) said that they expect Azhar to recover quickly and back to action for the final two ODIs in Sydney and Adelaide.
Although regular vice-captain Sarfraz Ahmed would have stepped into the captaincy role , he was forced to leave the tour earlier this week in order to be with his ill mother in Karachi, cricket.com.au reported.
Pakistan, who have now lost their past 16 matches on Australian soil, will also be without their fast bowler Mohammad Irfan for the rest of the series.
However, veteran batsman Shoaib Malik is expected to return to the squad after having missed the opening match due to illness.
The visitors, who are currently trailing 0-1 in the series following their crushing defeat by 92 runs in the opening match, will play their second ODI on Sunday at the Melbourne Cricket Ground (MCG).
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