The family have repeatedly demanded information on the health of the British-Egyptian activist in recent days, after he escalated his months-long hunger strike to include water.
Abdel Fattah, a veteran pro-democracy and rights campaigner, is serving a five-year prison sentence for "spreading false news" by sharing a Facebook post about police brutality.
International concern has mounted since the 40-year-old also began declining liquids since Sunday, marking the start of the UN climate summit COP27 hosted by Egypt.
On Thursday, an officer told the activist's mother that he was "under medical intervention", but gave no other details.
Hossam Bahgat, founder of the Egyptian Initiative for Personal Rights (EIPR), the country's largest rights group, said the prison officer statement "means he is being force-fed".
Amnesty International said they were "worried" that medical decisions for Abdel Fattah were "not made by independent doctors free from interference and coercion by security."
The dissident's aunt, novelist Ahdaf Soueif, demanded that he be moved to the Qasr al-Aini University Hospital, Cairo's largest state medical facility, fearing the prison hospital "is probably not equipped" to care for a patient who has been living for months "on 100 calories a day."
British Prime Minister Rishi Sunak, French President Emmanuel Macron and German Chancellor Olaf Scholz have all voiced concern during the climate summit and called for his release.
United Nations rights chief Volker Turk has warned Abdel Fattah's "life is in great danger".
Activists at the COP27 summit in Egypt's Red Sea resort of Sharm el-Sheikh have posted widely on Twitter under the hashtag #FreeAlaa. Several figures have ended their speeches with the words "you have not yet been defeated" -- the title of the jailed activist's book.
On Thursday, hundreds of COP27 participants, dressed in white like Egyptian prisoners, chanted "Free him!" and "no climate justice without human rights!".
Others shouted "Free them all!" in reference to the 60,000 political detainees rights groups say are incarcerated in the country, many of them in brutal conditions and overcrowded cells -- accusations which Cairo rejects.
"We are carrying out this action to draw attention to those who are invisible, hidden behind high walls," one of the organisers George Galvis said.