Article 18, which promotes freedom of religion in Iran and documents the persecution of Christian converts, said Aida Najaflou, 44, fell from her top bunk in the early hours of October 31, fracturing her T12 vertebrae.
She was taken to Taleghani Hospital for an X-ray but returned to prison the same day on a stretcher, still in severe pain and without the surgery doctors recommended.
Protests from fellow prisoners later prompted officials to transfer her to Shahid Tajrish Hospital, where doctors again advised urgent surgery and physiotherapy.
Despite this, the group said Najaflou remains in prison without proper medical treatment.
Najaflou, who suffers from rheumatoid arthritis, had repeatedly warned prison authorities that climbing to the top bunk was unsafe, but her requests for a lower bed were ignored.
She was still recovering from a nine-hour operation when Ministry of Intelligence agents arrested her in February and has been denied adequate care throughout her detention, including during 65 days of solitary confinement in Ward 209 of Evin Prison.