"The public statements made by athletes who previously trained at the Karolyi Ranch are gut-wrenching," Abbott said in a letter calling for an investigation by the Texas Rangers into the facility in Huntsville, about 70 miles (115 km) north of Houston.
The facility has been used for regular training camps but USA Gymnastics said earlier this month it had cancelled training sessions and was exploring alternative sites until a permanent location is found.
The complex was opened by celebrated gymnastics coaches Bela and Martha Karolyi in the mid 1980s and played a vital role in making the U.S. women's team a dominant force in global competitions.
The number listed for the ranch was disconnected and neither Bela or Martha Karolyi was immediately available for comment.
Last week, disgraced longtime USA Gymnastics team doctor Larry Nassar, 54, was sentenced to up to 175 years in prison for abusing young female gymnasts who were entrusted to his care.
At his sentencing hearing in Michigan, about 160 of his victims gave harrowing accounts of the abuse they suffered at the hands of the Nassar, who served as the programme's physician through four Olympic Games.
Victims also said some of the sexual abuse took place at the ranch. It is located in the Sam Houston Forest and includes training gyms, a dance studio, housing for 300 athletes, coaches and administrators and a dining hall.
Four-times Olympic gold medallist and Texas native Simone Biles said this month she was sexually abused by Nassar and it would be too traumatic to return to Karolyi Ranch as she worked toward her goal of competing in the 2020 Tokyo Olympics.
"Those athletes, as well as all Texans, deserve to know that no stone is left unturned to ensure that the allegations are thoroughly vetted and the perpetrators and enablers of any such misconduct are brought to justice," said Abbott, a Republican.
Nassar also worked for Michigan State University and Michigan's attorney general named a special prosecutor on Saturday to lead an investigation of the school.
Federal legislation to protect young amateur athletes from sexual abuse, spurred by the gymnastics scandal, moved a step closer to enactment on Monday when the U.S. House of Representatives passed the bill.
(Reporting by Jon Herskovitz; Editing by Tom Brown and Frances Kerry)
