The mishap took place at about 8:35 a.m. in the St. Catharine Academy on Williamsbridge Road near Astor Ave. in Allerton.
All four injured were identified as students by WABC-7. Two were critically injured and two were in stable condition.
FDNY officials said there was no fire.
The school was founded in 1889 and is sponsored by the Sisters of Mercy of the Americas. It has an enrollment of about 470.