All 13 players are now self-isolating, and 10 more players identified through contact tracing are in self-quarantine but asymptomatic at this time, according to a statement from the university.
In addition, four players have tested positive for COVID-19 antibodies, the school said. The Centers for Disease Control and Prevention says it does not know if antibodies can prevent a second infection or, if so, how long the protection might last.
The 13 positive results include two players who tested positive last week when 58 players initially returned to campus.
According to Big 12 guidelines, the Longhorns were able to begin voluntary workouts on Monday.
Kansas State officials reported Wednesday night that eight Wildcats athletes have tested positive for COVID-19 out of 130 tested.
The NCAA on Wednesday approved plans for an extended preseason to give teams more time to hold walk-throughs. With the coronavirus pandemic wiping out spring practice for most teams, along with the usual required summer activities such as weight training and film study, schools want to make up for lost preparation time.
The Associated Press contributed to this report.