Baena was a housekeeper and assistant at the family's Brentwood estate for 20 years, and was reportedly pregnant at the same time as Maria Shriver.
Reports in the New York Times and Los Angeles Times do not identify Baena by name, but according to radaronline.com, sources confirm that she and her son are the ones identified in The Los Angeles Times article that broke the story.
NBC station KGET reported that Baena and her son now live in Bakersfield, about 100 miles north of Los Angeles. The child is "about 14 years old," The New York Times reported, noting that Schwarzenegger and Shriver's youngest child, Christopher, is 13.
Monday's announcement by the former governor stunned many, but it wasn't the first time Schwarzenegger has faced allegations of infidelity.
Rumors on the campaign trail
Eight years ago, whispers about an out-of-wedlock child reportedly raised eyebrows among advisers as then-actor Schwarzenegger traversed California in a bid to unseat Gov. Gray Davis.
In the final days of the race, the Schwarzenegger camp — aided in large part by Shriver's vociferous defense — fought back against what many saw as more credible allegations that the actor had groped women during his years as one of Hollywood's leading men.
Monday night, responding to questions from The Los Angeles Times, the former governor released a statement admitting the affair and child with his staffer. In a statement released Tuesday, Shriver, a former NBC News correspondent, asked for privacy.
"As a mother, my concern is for the children," she said. "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."Video: Schwarzenegger hopes to regain family’s trust (on this page)
The news stunned many, but according to reports, it was no surprise to those who worked for Gov. Davis.
Garry South, a Democratic consultant in Los Angeles, told the New York Times that when the former actor indicated he may run for office, "there were rumors coming to us constantly about affairs and children." According to the same report, Schwarzenegger threatened to sue South, who worked for Gov. Davis at the time.
Peter Ragone, another former Davis adviser, told the New York Times: "There were all sorts of rumors flying around like this. Voters knew what they needed to know on this topic with Arnold Schwarzenegger, and honestly they just didn’t care."
A rocky legacy
Even before the admission, Arnold Schwarzenegger's political legacy in California was tenuous, at best.
He left the governor's office after seven years without making good on his central campaign promise to fix the state's budgeting system, then commuted the manslaughter sentence for the son of a political ally in one of his final official acts, drawing the condemnation of prosecutors and the family of a slain college student.PhotoBlog: Arnold Schwarzenegger and Maria Shriver in happier times
Now he's revealed to be the father of an out-of-wedlock child, a secret he kept during two gubernatorial terms.
After leaving office in January, the former Republican governor had for a time been angling for a role as some kind of international political spokesman, perhaps on environmental issues.
In April, he appeared at a Washington, D.C., forum on immigration hosted by President Barack Obama, but his grander plans for politics did not appear to be panning out, so Schwarzenegger lately has been trying to relaunch his career as a Hollywood action star.
No matter his accomplishments in office, Schwarzenegger may be best remembered as yet another philandering politician who got caught.
"It's over. There's no political future," said Patrick Dorinson, a Republican who worked on Schwarzenegger's 2003 campaign and in his administration early on. "I'm just disgusted. It's the only dang bipartisan thing these guys do — cheat on their wives. John Edwards, Arnold Schwarzenegger — tell me the difference."
However, producers of Schwarzenegger's upcoming Hollywood projects said they would not be affected by the news.
"The Governator", a collaboration between A2 Entertainment, Archie Comics and Stan Lee's Pow! Entertainment, has already sold into several foreign territories and awaits a U.S. network.
It stars Schwarzenegger as a superhero with a crime fighting lair beneath his Los Angeles house.
Schwarzenegger "creates a secret identity beneath his home — so secret that even his wife, Maria, and kids are unaware," says the press release for "The Governator", adding he is "a superhero living a double life, who's also a devoted family man who needs to make it home for dinner every night."
The Associated Press and Reuters contributed to this report.