But others supported the idea and said it could give the youngster the chance of a better life.
"Why not? At least the child will have a normal life," said Lyudmila Batikhina, a medical assistant at the orphanage.
Irina Kuzmenko, a student in the city of Donetsk said she envied the boy for being picked out by the wealthy singer.
"Does it really matter who your parents are as long as they love you?" she said.
"I want him to adopt me too," she joked.
Ukraine has one of the fastest rising HIV rates in Europe.
Two years ago Sir Elton gave a free concert in the main square in Kiev attended by tens of thousands of people to raise awareness of HIV/AIDS in the country.