The former Manchester United goalkeeper had held the role since 2016 and oversaw a successful period for the club, including reaching the Champions League finals in the 2018/2019 season.
But Ajax endured a disappointing season this term, finishing a distant third in the Eredivisie and failing to qualify for the Champions League.
Van Der Sar, who won the Champions League as a goalkeeper for Ajax in 1995, has taken the decision to step down immediately after a challenging period.
"After almost eleven years on the board, I am done," Van der Sar said.
"We have experienced wonderful things together, but it has also been an incredibly tough period. I am very grateful for the people I have met and worked with during my second career at Ajax, and what we have achieved and been through together.
"I feel the need to take some distance, to get some rest, and to do other things. It doesn’t feel good to take decisions about the future of this wonderful club in the coming period. That is why I have decided to resign."
Board member Pier Eringa added: "We wanted Edwin to stay, but he had made his decision. We have to respect that. The last season does not reflect the entire period that he has been in charge of Ajax.
"The club has seen a lot of success, has seen a lot of growth, and gained international exposure. His tasks will be transferred to the remaining members of the board.
"Edwin will be available for the transfer and advise until August. We expect to announce a new Board of Directors after August 1.
"It's our ambition to add someone to the board with an Ajax background."
