A statement on BTselem's website said Abu Rahma stated that the bullet hit his left toe.
The Israeli army admitted one of its soldiers had fired the shot and called the incident "a stark violation" of its rules of conduct.
"The injury was sustained when an IDF [Israeli army] soldier fired an anti-riot weapon in close proximity to the detained Palestinian man, who had been arrested for taking part in a violent riot," the statement said.
The army said it would investigate the incident.
The rights group said the incident took place on July 7, in the village of Nilin in the West Bank and had been filmed by a fourteen-year-old Palestinian girl in Nilin.