Authorities said the patient works at a pet shop in Causeway Bay, and the building she lives in in Aberdeen was locked down on Sunday night for testing but no other cases were found.
Speaking on a radio programme, Chan said although the number of daily coronavirus cases dropped recently, there are silent transmissions in the community.
In light of the recent discovery of local Covid-19 cases, the government had announced the cancellation of Lunar New Year fairs across Hong Kong.
Chan urged people to avoid crowds and do their new year shopping quickly ahead of the holiday.
She expressed hope that life will return to normal after the Lunar New Year.
A specialist in respiratory medicine, Leung Chi-chiu, told an RTHK programme that the Delta variant was likely to have leaked from a quarantine hotel following a cross-infection, because it had been a long time since the variant was detected in the community.
He said officials should trace the source quickly based on genome sequencing.
Leung said people need not worry about getting infected by both the Delta and Omicron variants at the same time, adding that the chances of this are very slim.
A virologist at the University of Hong Kong, Jin Dong-yan, also said the chance of people in Hong Kong being infected by both variants simultaneously is very small.
Jin said if a person is infected by Delta, for example, then he or she will normally have natural immunity against other variants of Covid-19.