According to the strictly-Orthodox Behadrei Haredim news site, it was the first day that one of the two attended the nursery.
Many of the children were said to be suffering breathing problems.
Reports said the two babies were in a separate area from the other children at the nursery that was located in a number of adjacent apartments.
Three caregivers have been detained for questioning.
The nursery was located in an apartment on Ha’Mem Gimel Street, a strictly-Orthodox area of Jerusalem.
Medics told Hebrew-language media that they were running in and out of the building, carrying multiple babies and young children at a time.
Police told the public to avoid the area.
This is a breaking story