International Christian Concern says there has been a surge in incidents in the last two months with little help from the authorities.
Chilling videos have been published online of teenage girls saying they chose to run away and convert.
But the families left behind and the ICC say victims are being beaten and raped before being blackmailed into taking part in the videos.
The ICC says Upper Egypt is "paralysed" by the number of disappearances of young girls.
One victim Mary Wahib, 18, was snatched from her home in the village of Bait Alaam at gunpoint by four masked men.
Four days later Mary appeared in a video on Facebook saying: "I bear witness there is no god but Allah, I bear witness that Muhammad is his messenger."
She claimed she had not been kidnapped and decided to convert to Islam.
Her cousin said: "We are sure that Mary was kidnapped and forced to appear in this video.
"We urge the officials in the state to intervene and return Mary to us."
Mary's family, who are Coptic Christians held a demonstration outside the local police station in a desperate bid to get the police to take action.
Married women in their twenties have also been taken captive and families have complained that the local police have failed to help them track down their loved ones.
In a similar incident a 19-year-old Amal Shaky was snatched on her way to Cairo University.
The ICC says police suggested the girl's father had killed Amal and thrown away the body.
Officers have since said they are investigating the disappearance but her father Zakaria fears she will be killed or forced into a Muslim marriage before she is found.
He said: "More than 40 days have passed since my daughter was kidnapped, and they say that the matter is under investigation.
"I don't know how long I should wait. Wait until they tell me that my daughter is killed or got married?"
A spokesperson for the ICC said: "ICC condemns these monstrous actions by radical Islamists in Upper Egypt and the lack of response on the side of local authorities . We weep with the families who have lost daughters, sisters and wives and pray their loved ones be returned.
"These perpetrators cannot continue to enjoy impunity. We call on the Egyptian authorities to ensure that justice is served and that maximum effort be put forth to curtail this wave of terror."
Concerns have been raised over human rights abuses in Egypt with Human Rights Watch reporting security forces recently tortured and arrested 20 people, including eight children, in Alexandria for demonstrating without permission.
The Coalition of Coptic Egypt, a Coptic advocacy group, says the Upper Egyptian province of Qena saw 72 cases of kidnappings, extortion and related violence against Copts in the period from 2011 to 2014.
It comes as tensions escalate between the Coptic community and violent Islamist groups and Christians in Egypt are said to be at a very high risk of persecution.
Open Doors UK, a Christian charity, says Egypt is the 22nd most dangerous country in the world for Christians.