Mohammadi was transferred from prison to hospital on Friday following a "catastrophic deterioration of her health, including two episodes of complete loss of consciousness and a severe cardiac crisis," a foundation run by her family said.
The Narges Mohammadi Foundation said the transfer was an "unavoidable necessity after prison doctors determined her condition could not be managed on-site".
Mohammadi, who is in her 50s, won the Nobel Peace Prize while in prison for her campaign to advance women's rights and abolish the death penalty in Iran.
She suffered a suspected heart attack in late March, her family said.
In an update on Saturday, the foundation said she remained in an unstable condition, receiving oxygen.
It called for her to be transferred to a hospital in Tehran for tests and specialised treatment.
Reuters could not independently confirm her condition.
Iranian authorities must release Mohammadi to her dedicated medical team so she can urgently receive treatment as her life is at risk, said Joergen Watne Frydnes, chair of the Norwegian Nobel Committee, which awards the Nobel Peace Prize.
She "is imprisoned solely for her peaceful human rights work. Her life is now in the hands of the Iranian authorities," he told Reuters on Saturday.
Mohammadi was sentenced to a new prison term of 7.5 years, the foundation said in February, weeks before the US and Israel launched their war against Iran.
The Nobel committee at the time called on Tehran to free her immediately.
On Friday morning, Mohammadi fainted after days of dangerously high blood pressure and severe nausea, the foundation said.
After multiple bouts of vomiting, she blacked out and was moved to the prison medical unit for emergency intravenous fluids.
The activist, who has undergone three angioplasty procedures, faces a "direct and immediate" threat to her right to life, her family said.
"We call for all charges to be dropped immediately and for all sentences imposed for her peaceful human rights work to be unconditionally annulled," the family said.
