Counsell said on Monday that both players are asymptomatic.
This marks the second setback for Urias since the Brewers acquired him from San Diego in November. Urias, who is expected to compete with incumbent Orlando Arcia for the starting shortstop job, underwent surgery in January to repair a broken bone in his left hand.
Major League Baseball and the players' association announced Friday that 31 players and seven staff members tested positive for the coronavirus during intake for the resumption of training, a rate of 1.2%.
The Nationals and Astros canceled their workouts Monday because they hadn't received results of their tests -- which were administered Friday.
Teams resumed workouts Friday for the first time since the coronavirus interrupted spring training on March 12, two weeks before the season was to start.
The Associated Press contributed to this report.