The interview with police, done nearly a month after the February shooting, was made public Monday after local media fought to have it released, over objections from prosecutors and the defense.
The woman, identified as witness No. 9 in court documents, said she was fondled, groped and kissed by Zimmerman beginning when she was 6 and he was about 8, when they would see each other at family gatherings. She said it continued until she was about 16.
Zimmerman's attorney, Mark O'Mara called it an "uncorroborated, irrelevant statement" in court papers. He said in a statement Monday he would vigorously defend Zimmerman against the relative's allegations.
Prosecutors said they may want to use the interview, as well as a separate statement from the woman calling Zimmerman a racist, but they did not yet want it made public because it could influence potential jurors.
It was not clear where the alleged abuse took place, and prosecutors did not return a telephone call seeking comment about whether they planned to pursue additional charges. At least one legal expert said charges would be unlikely, in part because laws limit how long a victim can wait before bringing allegations to authorities.
Zimmerman, 28, is charged with second-degree murder in the Feb. 26 death of the 17-year-old Martin, who was unarmed when he was killed in Sanford, about 20 miles north of Orlando.
Zimmerman claims Martin attacked him. He has pleaded not guilty, claiming self-defense.
The interview was done March 20 as Martin's supporters began organizing protests nationwide, saying the teen was racially profiled because he was black. Zimmerman's father is white and his mother is Peruvian.
In the interview, the woman tearfully recalled watching movies at Zimmerman's house when he first reached inside her underwear. She said she went to sleep crying.
"I would try to push him off, but he was bigger and stronger and older," she said.
She said she was not raped, but the abuse happened over the next 10 years.
Around 2005, the woman's parents arranged to confront Zimmerman at a restaurant, after learning from her sister what happened. He showed up, said "I'm sorry," and left, the woman said.
In a separate interview, the woman accused Zimmerman of being a racist.
"I was afraid that he may have done something because the kid was black, because growing up they always made - him and his family have always made - statements that they don't like black people if they don't act like white people," the woman said.
Under questioning, she said she couldn't recall any specific comments Zimmerman made.
The Orlando Sentinel, the Sun Sentinel and WFTV fought for the release of the interview, and the judge agreed.
"Adding this statement to the discourse will simply be another piece of the puzzle to be relied upon by those who want to believe there was a racial motive to the shooting, and will be dismissed by those who claim that there was no such motive" Circuit Judge Kenneth Lester wrote.
An attorney for Martin's family, Benjamin Crump, said the interview could be used at trial to show Zimmerman "has a history of violence and manipulation." But prosecutors and the defense attorney questioned in court documents whether it would be allowed.
Tamara Lave, a University of Miami law professor, said the allegations would be subject to whatever statutes of limitations were in place at the time.
"It's extraordinarily unlikely that even if the prosecutor wanted to file charges that she'd be able to do so," Lave said.
Prosecutors also released 145 phone calls Zimmerman made from jail. In one to his wife, he said he once wanted to be a priest, and he was thinking of becoming a chaplain.
Associated Press writers Jennifer Kay in Miami and Suzette Laboy in Fort Lauderdale contributed to this report.