The group were spotted in Sandall Park over the weekend and the volunteer group which looks after the park has told visitors to steer clear of the birds.
A spokesman for Friends of Sandall Park said: "At the weekend we were contacted by a concerned park visitor who said a family of children were picking ducklings up, much to the distress of their parents.
"This was witnessed and condoned by the parents of the children.
"Our volunteer then found an injured duckling on its own - apparently abandoned.
"Please do not pick up the ducklings and do not allow your children to interfere with them."