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.