The 25-year-old man handed himself in to police last night after officers found the white Nissan Patrol involved in the crash at a private property in Eden Park earlier that afternoon.
He is expected to be charged with traffic-related offences.
The six-year-old boy suffered a broken arm when the four-wheel-drive drove past and allegedly struck him on Brush Road in Epping at about 8.30pm on Tuesday.
Police believe the boy got out of a parked car and walked in front of the car onto the road when the Nissan allegedly crashed into him.
The driver told the boy’s carer his name was Frank and that he was unlicensed before driving off.
Police later alleged the man’s personal details were incorrect and the NSW registration plate attached to the car belonged to another vehicle.
The boy, from Epping, was later taken to the Royal Children’s Hospital to undergo X-rays on his arm.