The legendary goalkeeper suffered the stroke while on holiday in a Croatian island and had to be lifted to hospital by a helicopter, De Telegraaf reports.
Van der Sar was admitted to intensive care on Friday afternoon.
Ajax posted a message of support for their former CEO on Twitter, which read: “On Friday, Edwin van der Sar has had a bleeding around his brain
“He’s currently in hospital in the intensive care unit and is in a stable condition. Once there is more concrete information, an update will follow.
“Everyone at Ajax wishes Edwin a speedy recovery. We’re thinking of you.”
The 52-year-old, who won Champions League trophies with Ajax and United, stepped down from his role as CEO of the Dutch giants over a month ago. He initially joined his former side as marketing director in 2012 before being promoted to chief executive four years later.