Earlier this month, Cricket Australia announced that private investors would be introduced into the BBL from the 2027-28 season, beginning with the sale of the Melbourne Renegades Twenty20 franchise.
Baird, the former New South Wales premier, had spearheaded the privatisation push alongside CEO Todd Greenberg, following a review by Boston Consulting Group last year.
The move was criticised by Cricket New South Wales, which warned that it could reduce funding for grassroots cricket and weaken the sport's long-term development.
The Australian Associated Press reported on Monday that Baird did not wish to continue in his role without the support of all states.
"I believe Australian cricket continues to be well led by the CA Board. Their mix of significant experience and passion for the game gives me great confidence for the future," Baird said in a statement.
"This year CA will report record revenue, profit, attendance and viewership, and most importantly a 40 percent increase in participation over the past four years.
"I have been incredibly proud to play a role in the oversight of cricket on the CNSW Board and, over the past six years, the CA Board, including almost four as chair."
Former Australia opener David Boon, who played 107 test matches from 1984 to 1996 and scored 7,422 runs, is set to take over as Cricket Australia's interim chair from October 28.
"I am delighted that David Boon has agreed to undertake the interim chair role while we complete the formal chair process, and I will undertake a transition process with David over coming weeks," Baird said.