Club personnel who have recently been in close contact with the 19-year-old, including the entire senior team and coaching staff, will now self-isolate.
"Callum displayed symptoms similar to a mild cold on Monday morning and has not been at the training ground since then as a precaution," reads a statement from the Blues. "However, his test came in positive this evening and he will undergo a period of self-isolation. Despite testing positive for the virus, Callum is doing well and looking forward to returning to the training ground as soon as it is possible. ... We wish Callum a speedy recovery and look forward to welcoming him back to the club soon."
Confirmation the teenager contracted the virus came just hours after fellow London club Arsenal announced manager Mikel Arteta's COVID-19 diagnosis, with the Gunners also initiating self-quarantine procedures.
In response, the Premier League suspended all matches until April 4 after convening an emergency meeting.