Syed Raheel Farook, 31, was arrested in the early morning at his home in the California town of Corona, along with his wife Tatiana Farook, also 31.
Mariya Chernykh, Tatiana's 26-year-old sister who lives in the nearby town of Ontario, was also arrested.
The five-count indictment against the trio centers on Chernykh's alleged sham marriage to Enrique Marquez, who is awaiting trial on charges of aiding the December 2 attack carried out by Syed Farook and his wife Tashfeen Malik.
"This is the latest step in the comprehensive investigation into the horrific attacks in San Bernardino last year that took the lives of 14 innocent Americans and deeply affected so many more," US attorney Eileen Decker said in a statement.
"As I have said previously, we owe the victims, and the entire community of San Bernardino, a thorough investigation that uncovers all criminal activity surrounding these events."
The trio appeared in federal court after their arrest on Thursday and entered not guilty pleas, a Justice Department official said.
They were all given bail but were ordered to turn in their passports and banned from traveling outside Southern California pending their trial which was set for June 21, the official told AFP.
Marquez told investigators after his indictment in December on charges of buying weapons used in the San Bernardino assault that he had entered into a fake marriage with Chernykh in November 2014 and had lied about living with her.
Chernykh and her sister are both from Russia and Syed Raheel Farook's marriage to Tatiana has also come under scrutiny.
Syed Raheel Farook served in the US navy between 2003 and 2007 and is a decorated veteran.
His attorney Ron Cordova underlined before the judge at Thursday's hearing that the case against Syed Raheel Farook and his wife was about a "misrepresentation in an act of marriage, it's not about an act of terror.
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