The text submitted by more than 200 parliamentarians was sent to the Council of State, the parliament's website said, referring to the legal body which examines and amends legislation before it is ratified by the assembly.
Since the army ousted Islamist president Mohamed Morsi in July 2013, authorities have cracked down on all sorts of opposition, including human rights organisations.
The draft bill calls jail terms of up to five years and fines of up to one million Egyptian pounds ($63,300, 59,000 euros) for violations of the law, according to the heads of two NGOs who have seen the text.
"The organisations will not be able to carry out their activities without the prior authorisation of the administrative authorities," said Adel Ramadan, who heads the legal department of the watchdog Egyptian Initiative for Personal Rights.
If the draft bill becomes law, "NGOs will not be able to carry out a study or a survey without a permit from the state," he said.
"And another permit will be needed in order to publish the study or the survey," he said, adding that he also feared for the fate of charities whose work is far removed from politics.
Foreign NGOs will also have to pay up to 300,000 Egyptian pounds in order to have a presence in Egypt and apply for a permit which they will have to renew when it expires.
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The draft bill stipulates the creation of a "national authority" comprising representatives of the security services, intelligence and the army, who will oversee foreign funds and the activities of foreign NGOs.
"These are associations that help the government," Mona Gaballah, an MP for the liberal Free Egyptians Party, said.
"But this is a law for the national security of Egypt, put in place because questionable organisations with suspicious funding also exist."
Mohamed Zaree, head of the Egypt programme at the Cairo Institute for Human Rights Studies, said: "This is my worst nightmare, when I see such draft bills."
"They are closing the door on all organisations or associations which would have liked to deal with human rights in the future."
Human rights groups have repeatedly accused the government of President Abdel Fattah al-Sisi of violations, including forced disappearances, arbitrary arrests and illegal detentions.
Egyptian and foreign NGOs operating in the country are governed by a stiff law which allows the government to supervise their activities and finances.
In September a court froze the assets of five prominent human rights defenders and three NGOs, who had been under investigation for allegedly receiving foreign funds in a case dating from 2011.