Ashlyn was born with a host of respiratory issues and was diagnosed with 1p36 deletion syndrome, a rare genetic condition caused by a missing part of chromosome 1.
"I want to thank everyone for their thoughts and prayers," Robert Horry told the Los Angeles Times. "It means so much to our family."
The rare disease is characterized by intellectual disability, delayed growth, seizures and respiratory problems. Texas Children's Hospital spokeswoman Nicole Terry says Ashlyn Horry died there on Tuesday.
Horry played seven seasons with the Lakers from 1997-2003, winning three of the seven championships he collected in his 16-year career while with Los Angeles. His NBA career also included stints with the the Rockets, Suns and Spurs.
He earned the nickname "Big Shot Bob" for hitting several clutch shots in the playoffs and holds the record for 3-pointers made in the NBA Finals (53).
The Rockets selected Horry out of Alabama with the 11th overall pick in the 1992 draft. Horry helped the Rockets win NBA championships in 1994 and '95.
"My deepest condolences go out to Robert and his family on the tragic passing of his daughter, Ashlyn," Rockets owner Leslie Alexander said in a statement. "Ashlyn was born in Houston during Robert's time with us and I know he shared a special bond with her. The entire Rockets organization is saddened by her passing and our thoughts are with Robert and his family during this trying personal time."
Former Lakers star Magic Johnson offered condolences on his Twitter account.
"My thoughts go out to Robert Horry and his family as they deal with the tragic loss of his daughter Ashlyn," Johnson tweeted.
Horry finished his playing career in San Antonio, and won two titles with the Spurs to become the ninth player in league history to earn at least seven championship rings.
Horry and his family established the Ashlyn Horry Foundation to help other young people who are medically diagnosed with disabilities through economic relief and medical research, according to the foundation's website.
More information can be found about Ashlyn's condition and donations towards the cause can be made at http://www.ashlynhorryfoundation.org/.
Dave McMenamin covers the Lakers for ESPNLosAngeles.com. Information from The Associated Press was used in this report.