Both animals died Monday, The Miami Herald reported.
The tiger, Tevy, a 12-year-old female, was found dead in her enclosure, officials said. Tigers in zoos generally have a lifespan of 16 to 20 years.
"She wasn't a young tigress, but at 13 she still had some years ahead of her here at the zoo," Ron Magill, a zoo spokesman, told WBFS-TV. "She was a very key component to the breeding program we have here at the zoo. Now we are going to have to start from square one, basically, to try and get a mate for Hati, the other Malayan tiger here as a part of that breeding program."
Tevy was born in the Cincinnati Zoo and came to Miami from Knoxville, Tenn., four years ago. Veterinarians discovered Sunday she was suffering from jaundice and began treatment.
Mohan, the 44-year-old Indian rhinoceros, was believed to be the oldest of his species in captivity. Born in Nepal, he had been at the zoo since 1970.
"He was a very emotional loss for us," Magill said.
The decision was made to euthanize Mohan because he was having difficulty breathing and staying on his feet.
"He had not been on display for several years and had been retired and living in a quarantine area. He was just enjoying the final years of his life," Magill said.