It happened along the riverbanks near Pulaski Park around 6:21 p.m. on Wednesday.
The body of a 10-year-old boy has already been recovered.
An 11-year-old girl, the boy's sister, managed to get out of the water.
Marine units are combing the river along with drones to try and locate a 10-year-old girl who remains missing.
The other girl who is missing is their friend, the mayor said.
Passaic Mayor Hector Lora says the river's water level was higher than usual due to Tuesday's storms.
Lora also said that "the little boy may have saved" his sister's life.
"As he was going under, he pushed her, and she ended up by the rocks, so she climbed out," he said.
Lora said a man in the park jumped into the water to try and save them, but when he was about five meters deep, it was too deep, and the current pushed him away, and he could not reach them.