Veteran rights activist Mohammadi, 51, currently held in Tehran's Evin prison, was awarded the Nobel prize in October "for her fight against the oppression of women in Iran".
"Narges Mohammadi, today, through a message from Evin Prison, has informed her family that she started a hunger strike several hours ago. We are concerned about Narges Mohammadi's physical condition and health," her family said in a statement.
Mohammadi is refusing under any circumstances to wear a hijab, the head covering which has been obligatory for women in public spaces since shortly after Iran's 1979 Islamic revolution.
Prison authorities in response have refused to transfer Mohammadi, who suffers from heart and lung conditions, to a hospital outside Evin for treatment.
The family said in the statement that she was in "urgent" need of medical treatment outside prison.
"Narges went on a hunger strike today in protesting two things: The Islamic Republic's policy of delaying and neglecting medical care for sick inmates... (and) the policy of 'mandatory hijab' for Iranian women," the statement said.
"The Islamic republic is responsible for anything that happens to our beloved Narges," it said. "It's been a week now that they are refusing to give her the medical aid she needs."
'Morally unacceptable'
In a strong statement of support for Mohammadi, the Chair of the Norwegian Nobel Committee, Berit Reiss-Andersen, said the committee was "deeply concerned" about the 2023 laureate's health.
"The requirement that female inmates must wear a hijab in order to be hospitalised is inhumane and morally unacceptable," she said.
"Narges Mohammadi's initiation of a hunger strike demonstrates the seriousness of the situation. The Norwegian Nobel Committee urges the Iranian authorities to provide Narges Mohammadi, and other female inmates, with whatever medical assistance they may need," she added.
Pen International, a group promoting freedom of expression, meanwhile said it was "gravely concerned" about Mohammadi's health condition and "holds Iranian authorities fully responsible for putting her life at critical risk."
"Narges Mohammadi should not be in jail in the first place," it added, saying Iran should "immediately" release her and "urgently transfer her to a hospital to receive medical treatment."
'Means of repression'
First arrested 22 years ago, Mohammadi has spent much of the past two decades in and out of jail over her campaigning for human rights in Iran.
She has most recently been incarcerated since November 2021 and has not seen her children, now based in France, for eight years.
Mohammadi's Nobel came in the wake of months-long protests across Iran triggered by the September 2022 death in custody of Mahsa Amini, 22, who had been arrested for allegedly flouting the Islamic republic's strict dress rules for women.
From prison, Mohammadi has also expressed outrage over what she described as the "murder" of 17-year-old Armita Garawand who died in October after a month in a coma following an incident on the Tehran metro.
Activists say Garawand died after being beaten by the Tehran morality police for not wearing a headscarf, which has been vehemently denied by the authorities.
In a message expressing gratitude for the prize, read by her daughter and posted on the Nobel website earlier this month, Mohammadi described the mandatory hijab as a "means of control and repression imposed on society and on which the continuation and survival of this authoritarian religious regime depends".
