Mohammadi, 54, won the prize in 2023 while in prison for a campaign to advance women's rights and abolish the death penalty.
She suffered a heart attack two weeks ago.
Her family had called for her to be transferred from Zanjan, northwest of Tehran, where she was serving her sentence and where she had been initially taken to hospital, so that she could receive better medical care.
She is now at Tehran Pars Hospital for treatment by her own medical team after being transferred by ambulance, the Narges Mohammadi Foundation said in a statement.
Mohammadi's husband Taghi Rahmani, who lives in Paris, said on Saturday that her condition remained critical.
In a post on X, he wrote that she had suffered a severe drop in blood pressure and was now struggling to speak.
Mohammadi was sentenced to a new prison term of seven and a half years, the foundation said in February, weeks before the United States and Israel launched their war against Iran.
The Nobel committee at the time called on Iran to free her immediately.
She had been arrested in December after denouncing the death of lawyer Khosrow Alikordi.
A prosecutor told reporters that she had made provocative remarks at Alikordi's memorial ceremony.
The foundation gave no details of the bail arrangements or suspension of her sentence.
"However, a suspension is not enough," it said.
"Narges Mohammadi requires permanent, specialised care. We must ensure she never returns to prison."
Iran shut down most of the internet in the country in January as authorities suppressed mass protests triggered by economic unease.
Rights groups have reported ongoing executions of people involved in the unrest.
with DPA
