The boy's father told police he had sent his son on the errand.
Police were still talking to witnesses today and asking anyone who saw the shooting to come forward.
Investigators believe the motive for the shooting was robbery, but had not identified any suspects.
The victim, who was also shot in the right arm, was taken by helicopter to John Muir Medical Center in Walnut Creek, where he remained in critical condition today and unable to talk to investigators, LaDue said.
Police received a report of the shooting shortly after 5 p.m.
When officers arrived, they found the victim near the Wal-Mart parking lot, located at 4893 Lone Tree Way, but determined the shooting had occurred in the nearby park.
Some witnesses who heard the shooting told officers they had heard what they thought were fireworks, LaDue said.
Anyone with information about the case is asked to call the Antioch Police Department at (925) 778-2441.