Mirela Rupic, 36, filed the lawsuit after Visnjic refused to recognize the child as his, Rupic's lawyer, Nenad Skare, told The Associated Press on Friday.
Visnjic, who plays Dr. Luka Kovac on the long-running NBC series, has been married to Ivana Vrdoljak since 1999 and lives in Los Angeles. The couple told Croatian media last spring they have adopted a boy, born in April, in the United States.
Skare said that Rupic initially wanted to settle the matter directly with Visnjic, but her attempts failed. If Visnjic formally denies paternity, they would request a paternity test, Skare said.
Rupic told Friday's Jutarnji List that Visnjic "knew about my pregnancy from the start." The newspaper quoted her as saying she decided to sue him after he told her recently he would financially support the child, but never recognize her as his own.