The two-year-old is in a serious condition while his brother is in a moderate condition.
Edible forms of cannabis, particularly in high concentrations, can be harmful, especially to children.
Paediatricians say that such edibles should be clearly labelled and stored safely away from children like other medications and toxic products.
Medical cannabis to treat certain illnesses has been available to permit holders in Israel since the 1990s.
Recreational use of marijuana remains illegal, although it was partially decriminalised in 2017 with first-time offenders being subject to fines and treatment rather than criminal charges.
