"The Longhorn medical staff will monitor the situation and COVID-19 testing will continue as a plan for some team activities is reviewed," the Longhorns said Wednesday.
The school also said "all meetings Thursday will be virtual and team practices will not take place for the next several days, beginning with [Thursday's] scheduled morning workout."
Texas started spring practice Tuesday in Austin.
The Longhorns enter the season under new coach Steve Sarkisian, who was hired in January from the Alabama coaching staff. They posted a 7-3 record last season. The Longhorns went 32-18 in four seasons under former coach Tom Herman.
The Longhorns are scheduled to host Louisiana in their first game of the regular season Sept. 4 at Darrell K. Royal-Texas Memorial Stadium in Austin.