Three other cats had recovered from the virus, and one remained in critical condition Tuesday, he said.
The sanctuary said in a statement Friday that the facility was under quarantine and would be closed until further notice while the habitats were sanitized.
The virus began to present itself in November within the cougar population, with several cats developing pneumonialike symptoms. Within days, other species began to show signs of illness.
On Nov. 23, the first cat, a cougar, died, and several others began to become increasingly ill in the following days. An African serval was the last cat to die, on Dec. 13. Some of the cats shared a common wall between their habitats, but did not directly interact.
Only 17 cats remain in the sanctuary, Mathews said.
Mathews said that the sanctuary was working with officials to determine the virus's origin, though it has been difficult to pinpoint how it entered the grounds. Wild bird droppings might have entered the cat habitats, or the meat used to feed the animals could have contained the virus, he said.
"We have to go through and disinfect each habitat," Mathews said. "Any straw or organic matter needs to come out and be bagged and then burned, and then we have to disinfect again. Then we have to let it set for a couple weeks."
Workers at the sanctuary have been wearing protective clothing and N95 masks, and they are sanitizing their shoes to prevent any virus particles that could remain from spreading.
Cats are particularly vulnerable to avian influenza. A new version of the bird flu virus, H5N1, emerged in 2020 and has been rapidly spreading around the world, infecting birds and mammals.
The Washington Department of Fish and Wildlife said in a statement this month that it had confirmed bird flu infections in "numerous" wild birds this fall, and had recently confirmed that two cougars in another area, Clallam County, had the H5N1 virus.
The Wild Felid Advocacy Center in Washington takes in big cats who have not been properly cared for, or whose owners could no longer care for them.