Josey is said to be okay and is with family members.
Ventura County Sheriff's Department Capt. Eric Buschow, told the LA Times Josey was "in good health" following the ordeal.
"The family is going through a very traumatic time right now," Buschow said, later telling NBC LA: "This is considered to be a horrible accident.".
He said they were able to confirm Naya's identity after finding her wallet onboard the boat.
Naya's lifejacket is reported to have still been on the boat when Josey was found asleep, and Rivera's vehicle, a black Mercedes G Wagon, was later found in the car park with her handbag inside.
A Ventura County Sheriff's Department confirmed they had deployed air and dive teams to "search for [a] possible drowning victim".
Divers immediately started searching the lake, but so far there's no sign of the Glee star, and the search has been called off for the night and will continue tomorrow.
The actress, who starred as Santana Lopez in the series, recently posted a message on her social media accounts, eerily writing that "tomorrow is not promised" along with a selfie.
"No matter the year, circumstance, or strifes everyday you're alive is a blessing. make the most of today and every day you are given. tomorrow is not promised," the star posted to her 1.5 million followers last Friday.
Rivera also shared a photo of herself kissing Josey on social media, adding the caption: "Just the two of us" on Tuesday.
Following the alarming news, fans took to social media with an outpouring of support for the star and her family.
Others were furious to hear the search had been stopped until morning.
Rivera's life took a turn in late 2017 after she was arrested on domestic battery in 2017 against her ex-husband Dorsey following an altercation during which she allegedly hit him at their West Virginia home.
Dorsey claimed that Rivera struck him in the head and face, and hours after the alleged incident, her emotional court appearance was caught on camera for the world to see.
Law enforcement said at the time that alcohol was a factor in the incident.
The charge was dropped after Dorsey told prosecutors he didn't want to proceed.
E! reported that "Naya's friends and family (were) very concerned for her wellbeing" following the explosive incident.
The pair were married in 2014 but finalised their divorce in 2018 and share joint custody of Josey.
Glee has been plagued by controversy, heartbreak and scandal, earning it the title of the "Glee curse".
Glee's leading male Cory Monteith, who played Finn, died of a drug overdose in 2013 at the age of 31.
His co-star, Mark Salling, also another series favourite in the role of Puck, killed himself in January 2018. He was 35.
Salling was awaiting sentencing on child pornography charges at the time of his death.
Meanwhile the show has recently been in the headlines after star Lea Michele was publicly slammed for her behaviour to several of her co-stars.
Samantha Ware publicly confronted Michele, alleging she made her time on the show a "living hell".
Ware wrote that she would "never forget" the "traumatic microagressions" she claims to have received from Michele - including a shocking allegation that Michele had "told everyone that if you had the opportunity you would 's**t in my wig!'"
Ware has been fiercely supported by other Glee cast members with at least four coming forward backing her claims, including central cast members Alex Newell and Amber Riley.
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youth services: (06) 3555 906
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (available 24/7)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• CASPER Suicide Prevention
If it is an emergency and you feel like you or someone else is at risk, call 111.
