Mark Warner, the committee's Democratic vice chairman, issued a joint statement saying the panel chose to issue the subpoena after Flynn, through his lawyer, declined to cooperate with an April 28 request to turn over the documents.
Whatever the ultimate outcome of the Russian interference with the 2016 presidential election and the role of Gen. Flynn's connections with the Russians, Sally Yates' testimony that she brought the matter to Mr. Trump's attention has already raised speculation of a political future for her.
It was the first subpoena announced by the committee in its investigation.
"We were concerned that the American people had been misled about the underlying conduct and what General Flynn had done", she said.
Mr Warner had said on Tuesday the committee has been receiving documents as it investigates allegations that Russian Federation sought to influence the United States election, something Moscow denies.
Trump further maintained he desired to know "if there was a problem in the election having to do with Russia".
Federal prosecutors with the FBI have also issued grand jury subpoenas to Flynn, according to a report from CNN.
The acting chief of the FBI told the US Congress that Trump's shock firing of James Comey will not derail the investigation into alleged Russian meddling in the 2016 election.
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Flynn attorney Robert Kelner declined to comment on the newly issued subpoena or say why Flynn declined to provide the information earlier.
His ouster on February 13 after less than four weeks as national security advisor came after he was shown to have lied to Vice President Mike Pence about his sensitive talks with Kislyak.
Referring to Yates, a 27-year veteran of the Justice Department, Trump added, "I believe that it would be very unfair to hear from somebody who we don't even know and immediately run out and fire a general".
"That created a compromised situation, a situation where the national security adviser essentially could be blackmailed by the Russians".
The Trump administration asked for Flynn's resignation in February after the White House said he misled Vice President Mike Pence about a communication with Russia's U.S. ambassador Sergey Kislyak.
Mr Comey's sacking prompted a storm of criticism from Democrats, who accused the president of seeking to stall the probe.
Burr has said he was troubled by the Comey firing but would continue to press ahead with his investigation wherever it leads.
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