White Sox general manager Rick Hahn announced Wednesday that Abreu, the reigning American League MVP, is "completely asymptomatic" and "frustrated."
Hahn said that Abreu believes he "contracted a mild case" of the coronavirus last month, a belief that is "reinforced by the presence of COVID antibodies in additional testing."
"Other than being frustrated, Jose feels great and, like the rest of us, is looking forward to when he rejoins the club in the not too distant future," Hahn said.
Abreu, 34, is entering his eighth season with the White Sox and is expected to be the centerpiece of Chicago's powerful lineup.
The three-time All-Star led the White Sox to their first postseason appearance since 2008 last season, when he batted .317 with 19 home runs and led the majors with 60 RBIs.
La Russa: Abreu's health is first priority
White Sox manager Tony La Russa reacts to Jose Abreu testing positive for COVID-19.