The 49-year-old has served as director of football at top-flight Antwerp since March.
"Marc Overmars, director of football affairs at RAFC, became unwell last night and was admitted to hospital with a mild stroke," the club said in a statement.
"Marc is doing well in the meantime, but will have to take it easy for a while. Marc and his family focus on his recovery and do not wish to comment further."
Former Arsenal and Barcelona winger Overmars played for Ajax Amsterdam from 1992 to 1997 and became director of football at the Dutch club in 2012.
He stepped down from his job at Ajax in February, having admitted to "unacceptable" behaviour after sending inappropriate messages to several female colleagues.