Coronation Park in Oughtibridge was flooded at around 4pm following the persistent rainfall.
The floodwater has also overflowed to Oughtibridge Sports Club, which is located next to Beeley Woods and the river.
The sports pavilion at the club has also been left under water.
It is understood that the last time the playground flooded was when Sheffield received a one month worth of rainfall in 2019, which caused severe flooding across the city and the region.
Days of persistent rain, coupled with recent storms, have seen river levels rise on Sunday afternoon.
A number of flood alerts and warnings have been issued by the Environment Agency.
A stretch of the River Don in Sheffield city centre has already breached its banks between Nursery Street and the Riverside development.
Millhouses Park has also been shut as a safety precaution.