President Maithripala Sirisena presented the animal, named Nandi, to New Zealand Prime Minister John Key during his stop-over in Colombo on Wednesday.
It is the second time Sri Lanka has gifted a baby Elephant to New Zealand in 12 months.
Five-year-old Nandi will soon be relocated to Auckland Zoo to join Anjalee, the elephant gifted last year.
Hans Kriek, from Animal Protection Organization SAFE, told the New Zealand Herald, the elephant offering was more about "politics and international relationships than animal welfare".
"The cost involved with relocating and maintaining an elephant is so much higher than conserving animals in the wild," he said.
Auckland Zoo has welcomed the new addition to its attractions, but SAFE has been a long-time opponent of keeping animals in captivity.
The group had urged the zoo to reconsider housing elephants following the death of elephant Kashin seven years ago.
"Elephants do not do well in captivity. I can understand why the public would want to see them, by and large. But it's just a selfish thought," Mr Kriek said.
"They have a very limited area to the point where they have to be taken for walks to give them exercise."
Sri Lanka has given the same gift to Japan, China, South Korea, the Czech Republic and the US over the years.
