FC De Rebellen, a group including 38-year-old Drenthe, said on Instagram he had a stroke on Friday.
"He is receiving good care and is in good hands," their post said.
Reuters could not immediately reach his representatives.
"The team and everyone involved hope for a speedy recovery. Royston's family asks for peace and privacy during this period so they can offer him the necessary support and space for his recovery," the post added.
Drenthe, who retired in 2023, also had a spell in England, with Everton, Reading and Sheffield Wednesday.