The 49-year-old, who is currently sporting director of Royal Antwerp, went to hospital after becoming unwell on Thursday.
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The Belgian club insist he is 'doing well' but 'will have to take it easy for a while' as he begins his recovery.
"Marc Overmars, director of football affairs at RAFC, became unwell last night and was admitted to hospital with a mild stroke," a statement from Royal Antwerp on Friday read.
"Marc is doing well in the meantime, but will have to take it easy for a while.
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"Marc and his family focus on his recovery and do not wish to comment further. RAFC wishes Marc a speedy recovery!"
As a player Overmars won three Eredivisie titles and a Champions League with Ajax before joining Arsenal in 1997, where he won a Premier League and FA Cup double.
He then signed for Barcelona in 2000 before retiring in 2004. Overmars then briefly came out of retirement for a season with Dutch side Go Ahead Eagles in 2008. Overmars made 86 appearances across 11 years for the Netherlands.
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Overmars left his role as Ajax director of football in February after admitting to sending 'inappropriate messages' to female colleagues.
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