Shadab Khan will be Agha's deputy, the Pakistan Cricket Board has announced in naming squads for five T20s and three ODIs against New Zealand starting on March 16.
There was no place for senior batsman Babar Azam in the T20 side while Rizwan was also left out of a young squad as Pakistan look ahead to the T20 Asia Cup in September and next year's T20 World Cup.
Rizwan had only been named skipper of the white-ball teams in October.
Aqib Javed will stay on as interim head coach for the tour, extending his assignment beyond Pakistan's ill-fated Champions Trophy campaign on home soil, while the hunt for his successor begins. Mohammad Yousuf will join the squad as batting coach.
Hosts Pakistan ended their group campaign in the ongoing Champions Trophy without a victory and failed to reach the semi-finals.
Pakistan squads:
T20: Salman Ali Agha (capt), Shadab Khan, Abdul Samad, Abrar Ahmed, Haris Rauf, Hasan Nawaz, Jahandad Khan, Khushdil Shah, Mohammad Abbas Afridi, Mohammad Ali, Mohammad Haris, Muhammad Irfan Khan, Omair Bin Yousaf, Shaheen Shah Afridi, Sufyan Moqim and Usman Khan.
ODI: Mohammad Rizwan (capt), Salman Ali Agha, Abdullah Shafique, Abrar Ahmed, Akif Javed, Babar Azam, Faheem Ashraf, Imam-ul-Haq, Khushdil Shah, Mohammad Ali, Mohammad Wasim Jnr, Muhammad Irfan Khan, Naseem Shah, Sufyan Moqim and Tayyab Tahir.
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