The virus killed Apollo, a 12-year-old male tiger, and Layla, an 18-year-old lioness, last week after infecting 22 big cats at the In-Sync Exotics Wildlife Rescue and Education Center since June, The Dallas Morning News reported.
As of Sunday, three other big cats were in critical condition, said Lisa Williams, media director at the sanctuary.
The virus "came out of nowhere," said Lakshmi Nathan, chief volunteer at the center.
The big cats had been vaccinated for feline distemper, but not the canine version, Williams said.
"By the time we realized what was going on, the distemper had already spread out," Williams said.
Canine distemper starts respiratory system and then moves on to digestive system and nervous system and can cause seizures, the news report said.
There is no known cure for the virus, but volunteers are "doing everything that we can" for the animals, the rescue group said in a statement.
"Hopefully, these efforts will assist other facilities who may face this horrible disease in the future," the statement said.