The Black Swan star, 30, was said to be celebrating the birth of her first child with her French-born dancer fiancé Benjamin Millepied, a well known choreographer.
The couple, who met on set of the movie in which she won her Academy Award, have not released their son’s name.
, which broke the news, gave no details of where the baby was born or when. A publicist for Portman was unavailable for comment on Wednesday.
The Israeli-born, New York-raised actress, who celebrated her birthday last Thursday, announced in December that she was pregnant and planned to marry Millepied, 33, a well-regarded ballet dancer.
In Oscar acceptance speech in February, she paid tribute to "my beautiful love, Benjamin Millepied, who has now given me my most important role of my life."
She won in the best actress category for her performance as a delusional and a self-mutilating ballerina in Black Swan, Darren Aronofsky's psychological thriller.
Portman, who has stuck by a strict vegetarian diet, also won a Bafta best actress award although she did not attend because she was heavily pregnant at the time.
Although the pair are known for being protective of their privacy, they recently made public their joy at the prospect of becoming first-time parents.
“I have always kept my private life private but I will say that I am indescribably happy and feel very grateful to have this experience," Portman said when announcing her pregnancy.
She also admitted she would likely make “lots of mistakes but I am open to learning”. Despite her success with Black Swan, she told an interviewer in January
she would rather be at home.
“It's the most private of experiences, so I'd definitely rather be at home right now. But also, it's my job,” she said.
In another interview
she later said: “My back is not feeling great right now, sitting for so long. But everything’s really great otherwise.”
She admitted she stuck to tradition when it came to babies’ births.
“I think it’s a Jewish thing to be kind of superstitious,” she said in April. “You don’t do any of the baby stuff before the baby arrives.”
in an interview a few weeks ago, Millepied was effusive about his impending fatherhood.
"I'm going to take a lot of time off to enjoy this new stage of life that I'm really looking forward to,” he said.
“It's the unknown and there's something so exciting when you know life one way and you can do all kinds of projects and exciting things, but this is going to be so different and new and I love that idea.”
Portman rose to fame playing the preteen protegee of a hitman in "The Professional," and appeared in the "Star Wars" reboots as Luke Skywalker and Princess Leia's mother.
Portman was most recently in theatres with the romantic comedy "No Strings Attached”, starring as a overworked doctor who attempts to undertake a “casual” relationship with a “friend”, played by Ashton Kutcher.