The Ventura County Sheriff’s office said the 33-year-old was presumed to have drowned and the effort to find her was now classed as a “search and recovery operation”.
A huge search operation has been launched at Lake Piru in Southern California but she is yet to be found.
“Investigators believe Rivera drowned in what appears to be a tragic accident,” a police statement said.
Rivera’s son, who was found asleep and wearing a life vest on late Wednesday afternoon, told investigators that he and his mother went swimming and he got back on the boat, but “his mum never made it out of the water”.
Ventura Country Sheriff Sergeant Kevin Donoghue provided an update on Thursday and revealed CCTV from the dock shows Rivera’s boat departing.
He also revealed it may be weeks before any body is found. In the area where the boat was found, the water was about nine metres deep, he said.
Sgt Donoghue said: “If the body is entangled on something beneath the water, it may never come back up.”
He added: “There’s no way to really say.
“We’re putting our best foot forward to try and locate her, we’re using all the assets that are available to us, we’re using technology like Sonar, we have experts who have dove this lake that know it inside and out, that know where debris pockets might be.”
More than 100 rescuers are at the lake and involved in the effort to find Rivera, with “multiple dive teams” searching the murky depths while two helicopters continue to scour the waves from above.
Rivera’s family are waiting anxiously nearby for news, police said.
The most recent tweet from Rivera’s account, on Tuesday, read “just the two of us” along with a photo of her and her son.
Stars have shared prayers and messages of hope for the actress, who played cheerleader Santana in Glee.
Rivera’s Glee co-star Heather Morris posted a message for her former colleague on Instagram, writing: “We need all the prayers we can to bring our Naya back home to us. We need your love and light.”