The ex-Arsenal forward was "doing well", according to the club, which Overmars joined as sporting director in March.
Overmars, 49, "became unwell last night and was admitted to hospital with a mild stroke", the club said on its official Twitter account on Friday.
"Marc is doing well in the mean time, but will have to take it easy for a while. Marc and his family are focussing on his recovery and do not wish to comment further."
The club added that it "wishes Marc a speedy recovery".
Overmars left Amsterdam's Ajax in February after sending inappropriate messages and photos to female staff.
Antwerp appointed him a month later, saying they were giving him a "second chance".
Overmars made his name as a player at La Liga giants Barcelona and Premier League giants Arsenal.
© Agence France-Presse