The British actor confirmed he was set to become a dad again in July after enjoying a brief romance with the model earlier this year, while he was shooting Sherlock Holmes in New York.
Burke, who was due on Oct. 6, welcomed her daughter into the world on Tuesday night.
Law, who is currently starring in previews for a Broadway production of Hamlet, vowed to stand by Burke and help to raise the child, but was reportedly not present for the birth.
An insider tells People.com, "I doubt Jude was there. Besides the financial support, he's not involved."
Burke previously revealed she planned to call the tot Sophia.
The actor has three other kids with ex-wife Sadie Frost.
(c) 2009 WORLD ENTERTAINMENT NEWS NETWORK LTD. All global rights reserved. No unauthorized copying or re-distributing permitted.
