A lawyer for the family, Khaled Ali, said in a tweet he had been given permission to visit Mr Abdel-Fattah in prison and was heading there immediately.
It is the fifth day that the activist has gone without drinking any water or consuming any calories.
He later tweeted that he had been denied prison access to see his client by the Interior Ministry on Thursday.
The nature of the medical intervention was not known but the family has expressed fears prison officials would force-feed Mr Abdel-Fattah, which they said would amount to torture.
Mr Abdel-Fattah said in an earlier letter that he was prepared to die in prison if not freed.
His mother, Leila Soueif, said she spoke to prison authorities by phone and asked them if her son was undergoing any medical procedure and they said he was.
She asked "if it was by force, and they said no" and told her "Alaa is good," she said.
Ms Soueif called for him to be transferred to a civilian hospital rather than a prison facility. "I need proof for this. I don’t trust them," she said.
She has been waiting outside the prison every day this week, asking for proof her son is alive.
Mr Abdel-Fattah, who has been in prison for most of the past decade, is serving a five-year sentence on charges of disseminating false news for retweeting a report in 2019 that another prisoner died in custody.
He had been on a partial hunger strike of 100 calories a day for the past six months. He stopped all calorie intake and began refusing water on Sunday, the first day of the COP27 climate summit held in the Egyptian Red Sea resort town of Sharm El-Sheikh.
Egypt’s hosting of the event has drawn intensified international attention to heavy suppression of speech and political activity. Since 2013, President Abdel Fattah el-Sissi’s government has cracked down on dissidents and critics.
World leaders and activists have repeatedly called for Egyptian authorities to release the activist.
Mr Abdel-Fattah rose to fame during the 2011 pro-democracy uprisings that swept through the Middle East, toppling Egypt’s long-time president Hosni Mubarak. His long imprisonment since 2011 became a symbol of Egypt’s sliding back to autocratic rule under Mr el-Sissi.
Mr Abdel-Fattah’s younger sister, Sanaa Seif, has been at the conference, aiming to increase public attention on his case.
At the gathering, Prime Minister Rishi Sunak, French President Emmanuel Macron and German Chancellor Olaf Scholz raised the activist’s case in their talks with Mr el-Sissi. Mr Abdel-Fattah gained British citizenship through his mother, who was born in London.
Speaking to the AP on Thursday at the climate conference, Egypt’s foreign minister Sameh Shukry declined to answer questions about Mr Abdel-Fattah and suggested some countries were using the issue to distract from climate commitments.
"Other issues that are not directly pertaining to the climate might detract from the attention and ... give justification to maybe those who would prefer to concentrate on other issues to avoid having to deal with what they need to do, how they need to implement their obligations and responsibilities," he said.
"So, again, it is up to the parties to put the emphasis on the issues that are most important to them.”