NBC News reported that Salazar declined to say how Nunez died, but said the manner of death, along with other evidence in the cell, led to the conclusion his death was self-inflicted.
Salazar said Nunez’s death would not stop the investigation into the allegations against him.
"This alters things a bit, but it doesn't change our ultimate goal of proving it or disproving it," Salazar said, according to the Express-News. "We owe it to this victim to keep following these leads and trying to prove these allegations."
The girl and her mother, who is an undocumented immigrant from Guatemala, remain in the United States. The mother is applying for a visa available to victims of crimes or their relatives who are cooperating with authorities, the Express-News reported.
"This is life-changing," Salazar said of the allegations against Nunez. "I don't think anyone would dispute that. We need to make sure she's OK and her mom's OK."
NBC News reported that Nunez was a relative of the girl and her mother.
Salazar said during a June news conference that Nunez was suspected of abusing the girl for months, or possibly even years. He was apparently able to keep his behavior secret for so long, at least in part, because of the looming threat of deportation.
"The details of the case are quite frankly heartbreaking, disturbing, disgusting and infuriating all at the same time," Salazar said in June.
The sheriff said it was not clear at that time if Nunez was purposely targeting members of the Hispanic community who were undocumented, but he indicated that they can be seen as easy targets.
"Certainly, what was appealing was the vulnerability of that community because they are less apt to report things," Salazar said.
Deputies learned of the allegations after the mother took the girl to a fire station and reported the alleged assaults. Nunez was arrested on a charge of super aggravated sexual assault following an investigation.
Nunez was being held in Karnes County due to a departmental policy that requires Bexar County deputies charged with crimes to be housed in another agency’s jail.
"It could lead to allegations of favoritism, or it could be a bad situation in which you're guarding these inmates one day and the next you're one of them," Salazar told the Express-News.
The newspaper reported that Bexar County has a contract with Karnes County that allows up to 100 inmates to be housed there at a time. Nunez was one of just a few being housed in Karnes County at the time of his death, Salazar said.