"@rihanna you look so ugly tryin to be white," Bynes tweeted in a message she deleted two minutes later Sunday, X17 reported.
"Chris Brown beat you because you're not pretty enough," Bynes said in a later online message.
She also re-tweeted a post by Rihanna that read: "'Look who came to see me!! My lover Stella McCartney!!!," to which Bynes replied, "No one wants to be your lover so you call everyone and their mother that I almost named my new dog Rihanna."
X17 said Rihanna responded to the online insult with her own Twitter message.
"Ya see what happens when they cancel Intervention," she said.
"Unlike ur fugly faced self I don't do drugs! U need the intervention dog! I met ur ugly face in person! U aren't pretty u know it!" Bynes wrote.
Bynes, 27, is the former star of TV's "The Amanda Show" and "What I Like About You" and the films "What a Girl Wants" and "Hairspray." Her once-bright career has been eclipsed in recent months by reports of erratic behavior, bizarre online rants and motor vehicle offenses.
She was arrested last week in New York for allegedly throwing a bong out of her 36th-floor apartment window while police were in her home investigating a complaint that she was smoking marijuana in the building lobby.
Bynes later accused one of the police officers of sexual harassment, saying on Twitter he "slapped my vagina."
The matter is under investigation.
Celebrity Families of 2014 [PHOTOS]