The 'Expendables 2' star accepts he caused great pain to his now estranged wife Maria Shriver and their four children with his illicit romance, which led to Mildred Beana giving birth to his son Joseph 14 years ago.
He said in an episode of '60 Minutes' airing on Sunday: "I think it was the stupidest thing I've done in the whole relationship. It was terrible. I inflicted tremendous pain on Maria and unbelievable pain on the kids."
The former Governor of California is currently promoting his autobiography, 'Total Recall: My Unbelievably True Life Story' and though he says Maria hasn't read the tell-all tome, she wishes him the best.
He said: "I think that Maria is, you know, wishing me well in everything I do."
Mildred - who worked for Arnold's family for 20 years - had listed her ex-husband's name on Joseph's birth certificate and has previously said she only knew for certain who the boy's father was when he began to look increasingly like the actor.
The affair was only revealed in May last year, days after Arnold and Maria announced they were separating after 25 years of marriage.