The 33-year-old rented the boat on Wednesday afternoon at Lake Piru, north-west of Los Angeles, the Ventura County Sheriff's office said.
It said efforts to find the actress are now a "search and recovery operation". There are no signs of foul play.
Rivera is best known for playing cheerleader Santana Lopez in Glee.
The musical comedy TV series ran on the Fox network from 2009 to 2015.
What is known about the boating incident?
Rivera's child was spotted by another boater three hours after the actress had taken the boat, CBS Los Angeles reports, quoting the sheriff's office.
It says the boy told investigators that he and his mother were swimming - but she never got back into the boat.
The missing person was later formally identified as Naya Rivera, a Los Angeles resident.
The sheriff's department said the lake would be closed to the public as the search resumed on Thursday, with dive teams from across the region taking part.
On Thursday, Officer Chris Dyer of the Ventura County Sheriff's office said that authorities would be "switching efforts" to a search and recovery operation.
"We're presuming that an accident happened, we're presuming that she drowned in the lake," he said. "There are no signs of foul play, no signs that anything went wrong, besides a tragic accident."
Over 80 professional search-and-rescue personnel are still actively searching for Rivera, using helicopters, boats, and ground teams, police said.
"The goal is still to bring Ms Rivera home to her family so they can have some closure," Mr Dyer said.
On Tuesday, Rivera posted on Twitter a picture of herself and her son with a caption "just the two of us".
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