"To say this caught me by surprise would be an understatement," Gallagher said. "I played in last night's intrasquad game and felt great, and then received news this morning that my most recent test had come back positive.
"I am asymptomatic and will continue to work as hard as I can to stay ready while I quarantine."
The Royals are already without No. 1 backstop Salvador Perez, who's also sidelined because of the disease caused by the coronavirus.
Nick Dini is now slated to begin the season as Kansas City's starting catcher. The 26-year-old has played in only 20 career major-league games.