The shooting took place in Tran, a town 90km west of Sofia, Bulgaria's capital.
It is the worst case in a series of incidents over the past week at state homes for handicapped or abandoned children, where neglect and abuse are rampant, according to recent media reports.
On Sunday, a nine-year-old girl was badly hurt after jumping from the third floor of a children's home in central Sofia.
The next day, a 14-year-old boy from the same home was taken to a hospital after another inmate threw a stone at him.
Commenting on the shootings, Sergei Stanishev, Bulgaria's prime minister, promised to review legislation on the functioning of homes for children deprived of parental care.