Daniela Rajic, 24, gave birth to daughter Olivia on May 1 and filed the suit in Manhattan Family Court on Wednesday.
That night, George scored 37 points as the Pacers won Game 5 of their Eastern Conference finals matchup against the Miami Heat. Game 6 is Friday night in Miami.
George said during Friday morning's shootaround that the situation would not be a distraction to him or the Pacers.
The suit seeks a court-ordered DNA test and legal declaration that George is the father, and both newspapers, citing sources close to Rajic, said a private paternity test has affirmed that result.
Rajic's lawyer, Raoul Felder, told the Daily News that George has already met the baby and has voluntarily paid the medical bills.
The Post reported that George, 24, had a relationship with Rajic for a few months last summer after meeting in Miami, where she reportedly worked at Tootsie's Cabaret. Rajic has since moved to New York to be with her family, and she is currently a full-time mom.
Earlier this year, George dated Callie Rivers, the daughter of Los Angeles Clippers coach Doc Rivers.
A representative for George told the Post that "if and when the legal process confirms that the baby is his, he will fully embrace his responsibilities as a father and provide emotional and financial support to the child."