One staff member tested positive for the virus on April 16, and tests were subsequently conducted on its 29 children, a spokeswoman at Saiseikai Central Hospital, which runs the institution, said.
None of the eight children were showing major symptoms such as fever, but they had been hospitalised, she said.
Children who cannot live at home for reasons such as abuse, neglect or their parents' divorce are usually cared for at residential-care facilities in Japan.
The institution said seven of its 47 staff, including the person who already tested positive, had been asked to stay at home because of fevers or respiratory troubles.
Japan has had more than 11,500 coronavirus infections and nearly 300 deaths.