The post acknowledged Molek had touched the hearts of many zoo visitors, and encouraged people to share any "fond memories" people might have of the tiger.
Molek's cub Berani still lives at Auckland Zoo.
The zoo hoped he would adapt to his new situation as time went on.
The death came just months after the zoo euthanised two lions - the last two it had.
The elderly pair, 19-year-old Kura and her 17-year-old daughter Amira, were put down for their own welfare, a zoo spokesperson said in a statement.
"It is with great sadness we said goodbye to our two remaining 'golden girls'."
Carnivore team leader Lauren Booth said it would be "a very quiet Pridelands without their wonderful calls and we will miss their watchful faces".
"But they have left a wonderful legacy in the cubs they have had, the public they have inspired and the memories they leave with us."
Kura and Amira were the last lions left in Auckland Zoo's pride, after 19-year-old Sheeka was put down in November last year.