The 38-year-old man was held overnight while investigations into the incidents in Maltby continue.
South Yorkshire Police said three reports of a man in a car approaching children were made between 5pm and 5.50pm yesterday.
None of the children involved were harmed.
A South Yorkshire Police spokeswoman said: "A 38-year-old man has been arrested by police in Rotherham following several reports of suspicious activity in the Maltby area.
"Police received three separate reports between 5pm and 5.50pm from concerned members of the public reporting a man behaving suspiciously in Maltby.
"In the reports, a man driving a car is believed to have approached children."
The spokeswoman added: "The 38-year-old man remains in police custody at this time and an investigation is in its early stages, as officers work to ascertain the full circumstances surrounding each incident.
"Nobody is understood to have been injured and the children affected are receiving support."
Anyone with information should call South Yorkshire Police on 101 quoting incident number 755 of November 23.