PCSOs responded to a report on Thursday that a baby had fallen into the lake at Roundhay Park.
The family were feeding the ducks at the popular point, close to the Lakeside Cafe when the awful incident happened.
The baby was placed in the pushchair, but it did not have the brake fully applied. This then caused the pushchair to move and fall in, with the baby.
A passing member of the public assisted, and the baby was quickly rescued and taken to the cafe, where they helped care for both parties, until the paramedics arrived.
All were taken to the Leeds General Infirmary, where they made a full recovery.
Police warned the public to be careful when feeding the ducks.
A West Yorkshire Police spokesman said: "Please be careful. It is imperative to make sure that when feeding the ducks with pushchairs, that the brake is properly applied."