The woman, identified as Jane Doe this week in a court filing, said Rose called her in 1973, when she was 14 or 15, and they began a sexual relationship in Cincinnati that lasted several years. She also alleges Rose met her in locations outside Ohio for sex.
Rose's lawyer says the woman's claims are unverified.
The Phillies were going to induct Rose into their Wall of Fame in an on-field ceremony on Aug. 12. Rose bobbleheads were going to be distributed on Aug. 11.
The Phillies will not give away the collectibles and said fans with tickets for either game can exchange them or get a refund.
"While I am truly honored that the Phillies fans voted for me to be this year's Wall of Fame inductee, I am concerned that other matters will overshadow the goodwill associated with Alumni Weekend, and I agree with the decision not to participate," Rose said.
Rose, who was banned from baseball in 1989, made four All-Star appearances and helped the Phillies to one of their two world championships during his five seasons in Philadelphia from 1979-83.
Rose was selected through fan voting and was set to become the 39th inductee into the club's Wall of Fame.
"My baseball years in Philadelphia were amazing, not just because we won it all in 1980 and came close in 1983, but also because the fans welcomed me from day one," he said in April.
But public pressure against Rose played a role in the Phillies' decision to scrap the tribute.
The women's claim became public from testimony presented by the defense as part of a federal lawsuit Rose filed last year in Philadelphia against a lawyer whose investigation got the Cincinnati native kicked out of Major League Baseball for gambling.
Rose contends John Dowd defamed him by saying on the radio that the former baseball great had raped young teen girls during spring training. Rose has acknowledged having a relationship with the woman beginning when she was 16, the age of consent in Ohio.
Rose alleges in the lawsuit that Dowd damaged his reputation and endorsement deals during a July 2015 interview on WCHE-AM radio.
Dowd said during the radio appearance that Rose associate Michael Bertolini told investigators he "ran young girls" to Rose during spring training, which Dowd called "statutory rape every time," according to Rose's lawsuit. Bertolini's lawyers have denied that.
Rose acknowledged in a statement accompanying Monday's filing that he did have a relationship with the woman, but he said it started when she was 16. He also states they never had sex outside Ohio.
At the time, Rose was in his mid-30s and was married with two kids.
Rose's personal problems never seemed to affect his popularity in baseball. He's a regular on the autograph circuit and does broadcast work for Fox.
The Cincinnati Reds unveiled a bronze sculpture this season outside Great American Ball Park depicting Rose's headfirst slide. He was inducted into the Reds' Hall of Fame last June and had his No. 14 retired.
The 76-year-old hits leader is banned from baseball's Hall of Fame. Commissioner Rob Manfred has denied Rose's latest petition for reinstatement, but hasn't ruled out making him eligible for Cooperstown someday.
The fourth annual Philly Sports Roast also said it canceled its Aug. 10 event with Rose as the guest of honor. Tickets that started at $150 will be refunded.
The Phillies will still honor more than 40 alumni next weekend.
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