Major previously spent a short time in the spotlight when she was romantically linked last year to former reality television personality Jon Gosselin.
Michael Lohan confirmed his engagement to Major to the media Tuesday.
"I'm gonna vomit!" the younger Lohan told UsMagazine.com after hearing her father's news. "I so didn't need that info ... Yuck!"
Lohan starred in the hit films "The Parent Trap," "Freaky Friday" and "Mean Girls," but has in recent years been more famous for her hard-partying ways, trips to rehab and spats with her father.