The orangutan named Duchess was euthanized Sunday morning to prevent further suffering from the aggressive cancer, they said.
"She hadn't been doing well the last few days," zoo spokeswoman Linda Hardwick told The Arizona Republic.
Duchess was diagnosed with lymphosarcoma about two weeks ago after her keepers noticed a loss of appetite and lethargy and zoo vets said she had but a few weeks left to live.
Hardwick said a desire to give her some peace and preserve her dignity in her final days led to the decision to euthanize the orangutan matriarch.
Duchess has 14 descendants currently living at various zoos.
She lived roughly 22 years longer than the typical orangutan in the wild and about 12 years longer than those living in captivity, officials said.
"Although we are deeply saddened by Duchess' passing, she long surpassed the number of years that orangutans live in zoos and preserves, as well as in the wild," Bert Castro, the zoo's president and chief executive officer, said in a statement.