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The incident happened Sunday night in the stands at US Cellular Field, where the White Sox beat Houston in Game 2 of the World Series.
Biggio said his wife, Patty, wasn't hurt. He said the fan slapped his wife then tried to run away -- before the player's brother-in-law ended up "putting him against the wall."
Astros manager Phil Garner said that the fan had been bothering her for a while -- pulling Patty Biggio's hair and jostling her.
Guillen issued a public apology on behalf of his organization.
Chicago police say no criminal complaint has been filed.
Biggio played down an altercation.
"It was one guy who acted like a 12-year-old, who slapped her upside the head," said Biggio. "I'm not going to sit here and hold all the Chicago fans accountable for this for one guy who was acting like an idiot."
White Sox manager Ozzie Guillen said Monday he was going to personally apologize to Biggio on Tuesday.
"I know the security in Chicago is doing a great job and when something happens so quickly, you can't blame anybody," Guillen said. "And the guy that did it, he should be brought to Biggio and he's the one who can hopefully get him back.
"I told the police, 'Don't put him in jail, bring him to me in the dugout,"' Guillen said. "Hopefully, that won't happen again."