The 52-year-old was on holiday in Croatia when he became unwell. He was taken to hospital on Friday afternoon and is said to be in a stable condition.
The Dutchman left his role as chief executive at Ajax at the end of the season after a disappointing campaign.
Ajax posted a statement confirming their former player's condition.
The Eredivisie club said: "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."
Van der Sar spent almost ten years at Ajax from 1990-99. He had two seasons at Juventus before moving to England to sign for Fulham in 2001.
But he will mostly be remembered for his time at Manchester United where he made 266 appearences and won four Premier League titles, three League Cups and the Champions League in 2008 during six trophy-laden years.
He also won 130 caps for the Netherlands.
