A St John Ambulance spokesman earlier described the boy's injuries as serious but did not have specific details.
"We sent a rapid response and an ambulance to the scene which was an address on Main South Rd, Sockburn," he said.
"We have transported one patient, male, aged under 5 years, to Christchurch Hospital emergency department in a serious condition. We don't have specifics about his injuries."
Today, a police spokeswoman said the young boy's condition had improved.
"He's doing really well, which is a good thing," she said.
Asked if police were investigating, she it was in the hands of WorkSafe.
"It's got nothing to do with us. WorkSafe will begin their investigation tomorrow."
A spokesman for WorkSafe confirmed they had been notified and were making inquiries.
Kings Swim School director Todd Mason had not responded to approaches for comment this morning.
The pool's website says it offers swimming lessons for children and adults.
The purpose-built indoor facility is also available for hire "from a family birthday to a classroom session".