Zaid Alsalami, Shaykh Dr Zaid Alsalami is an Iraqi born scholar, raised in Australia. He obtained a BA from Al-Mustafa University, Qom, and an MA from the Islamic College in London. He also obtained a PhD from... Answered 1 year ago

Bismihi ta'ala

This would depend on the recommendation of a veterinarian or evaluation of a qualified person, as to whether the animal should be put down or not. If they believe that the animal pet should be put down, then it would be permitted to do so. 

And Allah knows best.