Hurley's spokesman told the BBC that both mother and child are "happy and healthy."
Since she announced her pregnancy in November, the 36-year-old Austin Powers star has been involved in a very public feud with Stephen Bing, the man she says is the baby's father.
According to Hurley, she and Bing were in an exclusive relationship when she became pregnant, but he has denied being the father and issued a public statement casting doubt on whether the baby was his. Bing says their 18-month relationship was "not exclusive."
Hurley insists she was faithful to Bing. "This is the first I had heard of this and the implications are very painful, especially as I am shortly to give birth to his child,'' Hurley said in a statement in December. "I'm deeply distraught."
Bing reportedly wanted a DNA test to prove paternity, which could only be carried out once the baby was born.
But Hurley later expressed hopes that the matter could be resolved without resorting to lawyers. Bing is a Hollywood producer and the grandson of millionaire New York real estate magnate Leo Bing.
If the baby is his, Hurley could collect millions of dollars in child support until Damian is at least 18.