Frances Lawrencina Anderson says she "had sexual intercourse" with the married director "on many occasions covering a period of time covering all possible dates of conception, including but not limited to December 2009".
Anderson's suit said she gave birth to their baby, Pearl Button Anderson, on August 30th of last year.
The filing said Soderbergh, 48, Anderson and Pearl "have submitted to a DNA test, which has confirmed that he is the father of the child".
Soderbergh's lawyer, Bernard Clair, said his client had voluntarily taken the DNA test, and was surprised by the legal action.
"My client is puzzled by the filing because they've been involved in settlement negotiations in Australia since April," the New York Post quoted him as saying.
He also said that there had been radio silence from Anderson's camp in the last two months.
"We view this filing as nothing other than an effort to forum shop because of the mistaken belief that New York will somehow be more generous to a baby that lives in Australia full time than the Australian courts," Clair said.
"If the filing was an attempt to intimidate, it has failed in a big way," he stated.
The suit says Soderbergh "has acknowledged that he is the father of the child verbally and by offering to pay various medical and other expenses incurred by Anderson in relation to the pregnancy", but seeks a formal declaration that he's the dad, as well as an unspecified amount in child support. (ANI)