Dee Gillin said she was walking along Mill Road, by the castle gates, at around 11.30am yesterday when she heard a woman shouting for help.
She went over to the stream's edge and saw the woman in the water trying to save her grandson, she said.
Dee believed he was about two years old, and as she could only see his head above the water she screamed out for help too.
Two men nearby ran across the road and helped the pair get the boy out of the water, Mrs Gillin said.
The 80-year-old praised the men for their heroism: "It was really bad, the kid was soaking wet and screaming.
"He was so frightened.
"If those two men weren't there, I would dread to think what would have happened."
The boy was taken back to Arundel Museum in Mill Road, where they stripped off his clothes and wrapped him in blankets.
Mrs Gillin said the grandmother told her they were feeding the ducks when the boy fell in the water.
She warned people to stay away from the edge.
She said: "Your own sense tells you not to go near the water, but putting a sign up saying don't go near the edge might help.
"The ducks all come out of the water when they see people with bread, so there is no need for people to go near the edge."