The young boy reportedly explained that he and his mum had gone swimming in the lake but his mother did not return to the boat.
Josey was reportedly spotted by another person visiting the lake, who noticed the boy was alone inside the vessel.
The 4-year-old is Rivera's only child, with ex-husband Ryan Dorsey, whom she divorced in 2018.
The Ventura County Sheriff's Department confirmed officers are searching for a presumed drowning victim at the scene after the child was discovered alone.
A rescue dive team and a helicopter with a drone have been dispatched to aid the search.
Rivera's life jacket was found in the boat, though her son was wearing his.
"They were seen going out on the lake together in the early afternoon, and approximately three hours after they left the dock another boater out on the lake discovered the boat drifting with the [son] on board asleep," Captain Eric Buschow, from the Sheriff's Department, told media.
"So they contacted the rangers and began an investigation and we've been actively searching for the mother since that time. We have both aerial search going on and our dive team as well.
"Indications are that we believe she did go in the lake. At this point it's still a search and that's what we know up to this point.
"The [son] said that he had been swimming with his mother and that he got back in the boat and [his] mum didn't," he added.
"We're going on the belief that she did go in the water, and we've not been able to locate her. This may well be a case of drowning.
"This is a big reservoir, it's deep, these kinds of things happen. We don't know all the circumstances. Investigators are working on that, getting as much information as possible."
