Ms Ebadi said her sister Nooshin, a medical professor, was arrested at home on Monday evening, and taken to prison.
She said her sister was only detained to prevent her own human rights work. Several journalists are also being held, according to opposition sources.
Earlier, Tehran rejected international calls for it to halt the crackdown.
On Monday, UK Foreign Secretary David Miliband hailed the "great courage" of the protesters and said it had been "particularly disturbing to hear accounts of the lack of restraint by the security forces" on Ashura, one of the holiest days in the Shia calendar.
'Punch on the mouth'
In response, Iranian Foreign Minister Manouchehr Mottaki said: "Britain will receive a punch on the mouth if it does not stop the nonsense."
The British ambassador has been summoned by officials to explain his country's "meddling" remarks, state media have reported.
The Revolutionary Guards, a powerful force tasked with defending the country's Islamic system, meanwhile accused foreign media of joining hands with the opposition and staging a "psychological war".
"Trying to overthrow the system will reach nowhere," the Isna news agency reported the Guards as saying. "Designers of the unrest will soon pay the cost of their insolence."
Iran's government says the violent opposition protests across the country on Sunday, in which at least eight people were killed, were inspired and aided by the West.
MPs have demanded "maximum punishment" for those involved.
'Blank warrant'
In a statement posted on the opposition website, Rahesabz, Ms Ebadi said her sister had been arrested at 2100 (1630 GMT) on Monday at her home in Tehran by four intelligence agents and sent to prison.
"I am not aware of the place of her detention or the reason for her arrest," Ms Ebadi said.
"Over the last two months my sister has been summoned by the ministry of intelligence several times and asked to convince me to give up my human rights activities. She was also told to move from her house, which is near my flat and they threatened to arrest her."
"My sister has not been involved in any social, human rights and political activities," she added.
Three journalists and a women's rights campaigner have also been detained, along with several senior opposition figures, according to opposition sources.
The prominent journalist, Mashallah Shamsolvaezin, was arrested at his home on Tuesday morning, according to the Rahesabz website.
"Six young men in plainclothes entered his house with a blank warrant, he resisted and asked for one with a name," it reported.
"But an hour later, four older men showed up and threatened to take him forcibly if he did not go with them."
'Iron fist'
On Monday, US President Barack Obama said the "iron fist of brutality" had been used to silence protesters, calling the actions of officials an "unjust suppression".
The authorities have blamed troublemakers for the violence, while the police have suggested that protesters may have shot each other.
On Monday, state-owned English-language Press TV said eight people had died. State TV had earlier reported that at least 15 people were killed.
The official death toll is the highest since June, when mass protests were sparked by President Mahmoud Ahmadinejad's disputed re-election.
Iranian security forces have been on alert since the influential dissident cleric, Grand Ayatollah Hoseyn Ali Montazeri, died 10 days ago.
His funeral attracted tens of thousands of opposition supporters, many of whom shouted anti-government slogans.
