Her husband, Reza Khandan, reported the news on his Facebook page on December 4.
The news led to expressions of joy on social-media sites among Iranians who had been following the case very closely.
For many it was a victory for Sotoudeh, who has refused to stay silent despite her time in jail and pressure on her family. A hunger strike is one of the few forms of protest that Iranian political prisoners have used in recent years to express themselves against the denial of some of their basic rights.
Iranian Nobel Peace Prize winner Shirin Ebadi, whom Sotoudeh has represented in court, told RFE/RL Radio Farda correspondent Jamshid Zand that "Sotoudeh's resistance" led to what she described as "her victory."
She said Sotoudeh's refusal to eat, which created domestic and international concern for her health, forced Iran's authorities to respect the law and remove the travel ban on her daughter.
Nevertheless, Sotoudeh remains in Tehran's Evin prison, where she is serving a six-year sentence for acting against national security and spreading propaganda, charges that many consider trumped up and linked to her work as a lawyer and rights activist.
The popular "Is This a Country We're Having?" Facebook page also welcomed the end of Sotoudeh's hunger strike by expressing what is on the mind of many of her supporters.
"I wish I could feel what you're feeling now. You felt what 70 million Iranians have never felt: the feeling of getting your rights from the Islamic republic."
Meanwhile, the Facebook page of Sotoudeh's husband has been flooded with messages of support and congratulation.
"Once again our Nasrin taught us a lesson. While facing injustice, instead of bowing to the authorities, we must force them to respect our rights," wrote one woman, apparently in Iran, who added that she's hoping for Sotoudeh's speedy release.
"Praise to Nasrin for her steadfastness," read another message posted on Khandan's Facebook page.