"Amanda seems to be doing well," the insider said. "The thing with Amanda is that it isn't as bizarre as it seems. She knows when to pull it together and act normal."
Fox News did not say what the actress' diagnosis is or how long she is expected to stay in the hospital.
Radar Online said Bynes' parents Rick and Lynn haven't spoken with the actress since she was hospitalized, but reported they are considering getting a conservatorship over her in order to help curb her erratic behavior.
Bynes, 27, allegedly caused a disturbance when she tried to break into a retirement community in her hometown of Thousand Oaks, Calif., last Sunday.
The following night, she reportedly set a small fire in someone's driveway, which led to police involvement and her eventual hospitalization.
"Deputies investigated the incident and determined that she met the criteria of 5150 W&I [California Welfare & Institutions Code.] She was detained and taken for a mental health evaluation,"
Capt. Don Aguilar of the Ventura County Sheriff's Office told Hollyscoop Tuesday.
The actress is known for her work on "The Amanda Show," as well as in the films "Hairspray" and "What a Girl Wants," but her last major screen credit was a supporting role in 2010's "Easy A."
Her once-bright career has been eclipsed in recent years by her bizarre Twitter rants and frequent brushes with the law.