The team said they are both doing well and are quarantining. They were both also vaccinated, according to the team.
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Bench Coach Andy Green will take over managerial duties starting with Friday's game against the Pirates at Wrigley Field.
The Cubs are among a handful of big league teams that have failed to reach the 85% vaccination threshold required for the relaxation of Major League Baseball's COVID-19 protocols, the Associated Press reported.
The announcement of the positive cases comes one day after the Cubs issued a COVID vaccine mandate for their non-playing employees, according to ESPN.
Those employees have to be fully vaccinated by Oct. 4, when staff return to their offices for the offseason. A source told ESPN that at least 90% of the team's employees are already vaccinated.
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The organization doesn't expect any high-profile departures due to the mandate.
The Chicago White Sox, meanwhile, had issued a mandate in June that personnel be fully vaccinated.
Because they are part of a union, MLB players are exempt from team mandates, as they have to be collectively bargained. The league and union are currently negotiating a new collective bargaining agreement. The current one expires on Dec. 1.
ESPN and AP contributed to this report.