Four-month old twins were admitted to the Sheba Medical Center at Tel Hashomer with multiple contusions, Ynet reported Thursday.
The hospital said overnight Thursday that one baby is in critical condition, while his twin sister's condition is stable.
Police officials said investigators suspect the toddlers were physically abused but are also examining other possibilities.
Doctors have ruled out the possibility that a virus attacked the infants, and confirmed they suffered numerous bruises all over their bodies. The parents have not been interrogated as of yet.
Gilad Morag contributed to the report