It is the first time Bannon has testified in the probe of whether campaign associates of the president colluded with Russian Federation in its bid to influence the 2016 United States elections. That subpoena, first reported by The New York Times, appeared to be a negotiating tactic that then prompted Bannon to agree to a sit-down with Mueller's prosecutors rather than appearing before the grand jury.
An incendiary book released last week, "Fire and Fury: Inside the Trump White House", by Michael Wolff, quoted him as saying that a pre-election meeting involving Trump's eldest son Donald Jr. and a Kremlin-linked Russian lawyer was "treasonous".
Bannon's attorney told the committee that Bannon would answer questions when he goes to the special counsel because executive privilege would not apply, according to a source who's familiar with the process with Bannon.
Bannon isn't the only Trump associate expected before the committee this week: Corey Lewandowski, Trump's first presidential campaign manager, is expected before the panel later this week.
Former White House Chief Strategist Stephen Bannon arrives for an interview by the House Intelligence Committee investigating alleged Russian interference in the 2016 U.S. election on Capitol Hill in Washington, U.S., January 16, 2018.
A second subpoena for Mr. Bannon to testify came from a House panel on Tuesday.
After the interview, Democrats on the committee accused the White House of exerting influence over Mr. Bannon to keep him from expounding about his time in the West Wing.
"We would later learn that would be extended to even after he left the White House", Schiff added.
"This was effectively a gag order by the White House preventing this witness from answering nearly any question concerning his time in the administration and many questions even after he left the administration", Schiff said. But it was not clear why Mr. Mueller treated Mr. Bannon differently from the dozen administration officials who were interviewed in the final months of past year and were never served with a subpoena.
Mr Bannon was not present at the meeting, nor during the drafting of the President's misleading statement on this issue - both of which are reportedly of interest to Mr Mueller.
But when the lawmaker's questions moved to Bannon's time in the White House, Bannon's lawyer got on the phone with the counsel's office.
A grand jury testimony is usually more taxing for the witness, as the entire proceedings are transcribed and the witness is required to answer every question. Bannon apologized a few days later, but was stripped of his job leading the pro-Trump news site Breitbart News.
Significant grand jury activity may undermine the case that White House officials have made for months: that they believe the inquiry is coming to an end and are convinced that the president will be cleared. He was also not present for the controversial firing of Mr Trump's former Federal Bureau of Investigation director, James Comey.
Bannon was first asked to testify before the panel prior to his rift with Trump.
Rumors have swirled that Bannon, while in the White House, was responsible for some of the most damaging leaks about Trump's son-in-law, Jared Kushner - including one about Kushner's meeting in December 2016 with the CEO of a sanctioned Russian bank.
Trump has said publicly several times that he has no intention of firing the special counsel.