The former California governor admitted in a statement earlier this week that his split from Maria Shriver was partly due to him fathering a child with a member of his household staff.
According to The Los Angeles Times, the employee worked for the family for 20 years and gave birth to the actor's child over a decade ago.
The article also notes that Maria moved out of the family's Brentwood home earlier this year, after Schwarzenegger acknowledged the paternity.
It is believed to be with his former housekeeper Mildred Baena
Arnold said in a statement to the publication: 'After leaving the governor's office I told my wife about this event, which occurred over a decade ago.
'I understand and deserve the feelings of anger and disappointment among my friends and family. There are no excuses and I take full responsibility for the hurt I have caused. I have apologised to Maria, my children and my family. I am truly sorry.
'I ask that the media respect my wife and children through this extremely difficult time. While I deserve your attention and criticism, my family does not.'
A spokesman for Shriver, 55, who was married to Arnold for 25 years, said: 'This is a painful and heartbreaking time.
'As a mother, my concern is for the children. I ask for compassion, respect and privacy as my children and I try to rebuild our lives and heal. I will have no further comment.'
Two of their four children posted on Twitter, expressing their love for their family.
'Some days you feel like s***, some days you want to quit and just be normal for a bit,' tweeted 17-year-old Patrick Schwarzenegger.
'Yet I love my family till death do us apart.'
His 21-year-old sister, Katherine Schwarzenegger, followed later in the day.
'This is definitely not easy but I appreciate your love and support as i begin to heal and move forward in life,' she said. 'I will always love my family!'