The health district says the bats were too damaged to be tested for rabies.
A statement from the district said the children are related to each other.
Another Eastern Washington child, an 11-month-old girl, was treated after she was bitten by a rabid bat earlier this month at her grandparents' Pasco home.
The health district says there have been two human cases of rabies in Washington in the last two decades. Bats are the primary animal carriers in this region.