An investigation is underway into the source of the virus, as health officials continue monitoring human contacts and other animal facilities.
The latest H5N6 case is China's fourth of the year.
The CDC said the risk of the virus passing from cats to people is small but possible, and they urged owners to monitor their pets' health.
Twelve fur farms in Finland have now been affected by H5N1 avian flu outbreaks.
As a pandemic preparedness step, two UK virologists call on governments to eliminate mink farming.
H5N1 avian flu has been detected on 5 more fur farms, including one housing silver foxes.
Surveillance in people who had contact with the sick cats found no illnesses, and the WHO said the risk is low to moderate for that group.
The two people had no symptoms and were exposed to sick poultry at different farms.
Blue fox are the most common fur animal farmed in Finland, and officials say wild birds are the likely source of the virus.
Though the virus hasn't shifted its preference to mammalian cells, scientists see some changes that could enhance replication and allow binding to human-like receptors.
