A Hawke's Bay District Health Board spokeswoman said the boy, who is in his teens, remains in a stable condition.
Go Bus Chief Operation Officer Nigel Piper said it "would not be appropriate" to comment on the incident due to an ongoing police investigation.
"We do however send our best wishes to the family and hope that their son has a speedy recovery," he said.
Piper added: "We are also offering the company's support to the wellbeing of our driver, who understandably is also affected by the accident."
Police said they received a report of an incident where a person reportedly jumped from a moving bus on High Street in Waipawa, about 3:30pm.