Mani previously represented the PCB at the International Cricket Council, cricket's governing body, as Treasurer for three years and later headed the body for another three years from 2003 to 2006.
Sethi, who has had longstanding differences with Imran Khan, said he had been waiting for the new prime minister to take oath before submitting his resignation.
"I wish PCB all the best and hope our cricket team goes from strength to strength," he tweeted on Monday. "Eid Mubarak. Pakistan Zindabad."
The text of his resignation recalled his appointment to the PCB's Board of Governors by ousted prime minister Nawaz Sharif from 2014 to 2017, and then again by former prime minister Shahid Khaqan Abbasi from 2017 till 2020.
He recalled that PM Khan "said on many occasions that you have a vision for Pakistan cricket."
"Therefore, it is only proper that you should assume charge and responsibility for assembling a management team for PCB that enjoys your full confidence and trust," he added.
"In order to facilitate your objectives in the interest of Pakistan cricket, I hereby submit my resignation as Chairman of PCB and Member of its BoG," the letter read.