Garcetti made the announcement during a coronavirus briefing from home.
"On Monday while I was at work, my wife called to let us know our beloved daughter Maya, who turned 9 this weekend, wasn't feeling very well," Garcetti said. "And after she came down with a fever, we had her tested for COVID-19 and her results came back positive."
He added that her symptoms are mild and she is doing fine. He and his wife have tested negative for the virus.
The mayor also said he and his wife will be quarantining and Maya will be in isolation for at least 10 days from the time she started showing symptoms.
Garcetti said he will be working remotely in the meantime.
The mayor does not know how his daughter contracted the virus. He added that the family has been following the proper safety guidelines and they have not been mingling with people outside their household.
Garcetti gave a stark briefing to city residents, warning that within days L.A. County may declare a systemwide crisis with all hospitals out of usual space and staffing. The hospitals are planning by identifying areas such as parking lots and conference rooms that can be used for patient care.
He also reminded residents that the governor earlier announced the state had ordered 5,000 additional body bags and has dozens of refrigerated trucks ready to use as temporary morgues to handle bodies too numerous for existing morgues.
"That frightens me, and it should frighten you," Garcetti said.
The announcement came on the same day as L.A. County reported 14,418 new coronavirus cases and 102 deaths.
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The Associated Press contributed to this report.