The order, unsealed Friday in federal court in Washington, D.C., confirms that Franklin has not been accused of any crime and has made two court appearances before a federal judge.
She was detained by federal agents on Sunday in St. Louis and transported to Washington and has been in custody since then.
Federal law allows judges to order witnesses to be detained if the government can prove that their testimony has extraordinary value for a criminal case and that they would be a flight risk and unlikely to respond to a subpoena. She lives in Tehran and comes back to the United States about once a year to see her family, usually scheduling documentary work in the USA, her son said.
The St. Louis office of the Federal Bureau of Investigation referred CPJ to the Department of Justice, which did not immediately respond to an email inquiry about the case.
The order does not specify which office in the Justice Department is involved in the case being investigated.
Hashemi came to the U.S.to visit relatives and to shoot a documentary, according to The Associated Press, which spoke to her son Hossein Hashemi.
Marzieh Hashemi, a US citizen who has lived and worked in Iran for much of her adult life, is being held as a material witness by the USA government.
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Hashemi married an Iranian man and converted to Islam.
"The arrest of Marzieh Hashemi by America is an unacceptable political act that tramples on freedom of speech", Foreign Minister Mohammad Javad Zarif said Wednesday.
The advocacy group said that Iran is detaining at least eight journalists over their work.
The incident comes as Iran faces increasing criticism of its own arrests of dual citizens and other people with Western ties. -Iranian journalist Jason Rezaian, a correspondent for The Washington Post.
Hashemi was born in New Orleans as Melanie Franklin in a Protestant African-American family.
She has been appointed an attorney, according to the order, and she has appeared before a U.S. District Judge twice.
According to a U.S. federal court order issued on Friday, Hashemi is not facing any legal charges herself, but is being detained as a material witness to testify in an ongoing criminal case, Reuters said.
The court order said that Hashemi, who was born in the United States as Melanie Franklin, had been detained to give a testimony to a jury investigating unspecified "violations of USA criminal law".