The Pakistan Cricket Board said all-rounder Salman Ali Agha will serve as Rizwan’s deputy, as reported by Reuters.
"I’m deeply honoured to be appointed as Pakistan’s white-ball captain," Rizwan said in a statement.
"Representing Pakistan on the global stage is the greatest privilege and to now be entrusted with leading such a talented and exciting group of players is a tremendous honour.
"I’m committed to giving my absolute best in this role and look forward to working closely with the selectors, coaches and my immensely talented teammates. Together, we aim to meet and exceed the expectations of our fans and supporters."
The 32-year-old Rizwan has played 74 ODIs and 102 T20Is since making his white-ball debut in 2015, scoring a combined 5,401 runs.
Babar stepped down as skipper in all three formats last year after Pakistan failed to make the knockout stage of the 50-overs World Cup, before returning as white-ball captain in March for the T20 World Cup where the team did not make the Super Eight.
He quit the role again this month, saying he needed to reduce his workload.
The batting mainstay as well as pace bowlers Afridi and Naseem were dropped by Pakistan for the last two tests against England due to patchy form and the team secured a 2-1 series win on Saturday.
The trio will not feature in the matches against Zimbabwe which follow the Australian series.
Wicketkeeper-batsman Rizwan will be available for the Australia games and the Zimbabwe ODIs, but will be rested for the T20Is, with Agha stepping in for him.
Pakistan will play three ODIs and three T20Is against both Australia and Zimbabwe. The Australia tour runs from Nov. 4-18, and the games in Bulawayo will be played from Nov. 24-Dec. 5.
Pakistan squads:
Australia tour:
ODIs: Aamir Jamal, Abdullah Shafique, Arafat Minhas, Babar Azam, Faisal Akram, Haris Rauf, Haseebullah, Kamran Ghulam, Mohammad Hasnain, Mohammad Rizwan, Muhammad Irfan Khan, Naseem Shah, Saim Ayub, Salman Ali Agha, Shaheen Afridi.
T20Is: Arafat Minhas, Babar Azam, Haris Rauf, Haseebullah, Jahandad Khan, Mohammad Abbas Afridi, Mohammad Rizwan, Muhammad Irfan Khan, Naseem Shah, Omair Bin Yousuf, Sahibzada Farhan, Salman Ali Agha, Shaheen Shah Afridi, Sufyan Moqim, Usman Khan.
Zimbabwe tour:
ODIs: Aamir Jamal, Abdullah Shafique, Abrar Ahmed, Ahmed Daniyal, Faisal Akram, Haris Rauf, Haseebullah, Kamran Ghulam, Mohammad Hasnain, Mohammad Rizwan, Muhammad Irfan Khan, Saim Ayub, Salman Ali Agha, Shahnawaz Dahani and Tayyab Tahir.
T20Is: Ahmed Daniyal, Arafat Minhas, Haris Rauf, Haseebullah, Jahandad Khan, Mohammad Abbas Afridi, Mohammad Hasnain, Muhammad Irfan Khan, Omair bin Yousuf, Qasim Akram, Sahibzada Farhan, Salman Ali Agha, Sufyan Moqim, Tayyab Tahir, Usman Khan.
