The boy, who is not thought to be the former Liverpool star's nine-year-old son, was rushed to Chester hospital on Wednesday (10 June) with a "serious but non-life threatening injury", the Mail Online reported.
A Welsh Ambulance Service spokesperson said: "We were called at approximately 7.15pm on Wednesday 10 June to reports a child had been injured at an address in the Northop area of Flintshire.
"We sent a paramedic in a rapid response car and an emergency ambulance to the scene, and the child was taken to the Countess of Chester Hospital with a serious but non-life threatening injury."
Passer-by Nick Rothe, who was walking his dog on a public path near the property, told the Daily Mirror that the boy "didn't look very good at all".
"There was one child injured. He was lying on the ground," he said. "Michael is a very private person and he doesn't like you talking to him so we didn't say 'can we help?'. Michael was there and I think his brother was stood over the child."
He added: "I had heard them screaming about on the quad bike. I have seen them doing it before. They tear around his front garden."
A spokesman for Michael Owen told the Daily Mirror: "The child in question was hurt but the emergency services dealt with it brilliantly and he is recovering well.
"There is nothing more we would like to add at this stage."