The 'Log Ride', which the amusement park's website describes as "one of the steepest and largest log rides ever built", involves a drop of 48 feet.
According to USA Today, the log shaped cart hit the bottom of the water slide with force, before flipping over and ejecting the family into the water.
Riverside Fire Department said in a Facebook post that all three individuals were treated at a local hospital.
Fire Captain Brian Guzzetta told KTLA-TV he understood the incident occurred because there was "no water flowing on the ride" following a pump malfunction which caused the family's cart to travel down the structure with excessive force and speed.
Castle Park shared a Facebook post about the accident, advising customers the Log Ride will remain closed until a full investigation can be carried out.