Michael Flynn has failed to voluntarily co-operate with the investigation, the committee says.
The national security adviser was forced to resign in February after failing to disclose the content of his talks with Russian diplomats.
Meanwhile, the fallout continues over the firing of the FBI director.
The White House maintained that James Comey was removed on May 9 for his handling of the inquiry over Hillary Clinton’s emails.
However, senior Democrats said James Comey had recently asked the justice department for more resources for his Trump-Russia investigation.
The Senate Intelligence Committee said it issued a subpoena after Michael Flynn rejected its request on April 28 to submit documents relevant to the investigation.
Michael Flynn, a retired army lieutenant-general, misled the White House about discussing US sanctions against Russia with the country’s envoy, Sergei Kislyak, before President Trump’s inauguration in January.
His links to Russia are being scrutinized by the FBI and the House and Senate Intelligence Committees, as part of wider investigations into claims Moscow sought to tip the election in favor of Donald Trump, and into contacts between Russia and members of the president’s campaign team.
Reaction to James Comey’s firing continued on May 10, with a White House spokeswoman saying that President Trump had been considering sacking the FBI director since he was elected.
Howver, critics accuse President Trump of firing the nation’s top law enforcement official because he was leading the Russian inquiry.
The White House has rejected calls to appoint a special prosecutor to investigate allegations the Trump campaign colluded with the Kremlin over last year’s election.
The Senate Intelligence Committee invited James Comey to testify next week.
In a farewell letter to staff, James Comey said he would not “spend time on the decision or the way it was executed”.
“I have long believed that a President can fire an FBI Director for any reason, or for no reason at all,” he wrote.
“It is very hard to leave a group of people who are committed only to doing the right thing,” James Comey added.
“My hope is that you will continue to live our values and the mission of protecting the American people and upholding the Constitution.”
President Trump stood by his actions, saying James Comey was fired “because he was not doing a good job”.
On May 10, Democratic senators Dianne Feinstein and Richard Durbin told media that James Comey had asked Deputy Attorney General Rod Rosenstein – who wrote the memo on which President Trump says the sacking decision was based – for more resources for the FBI investigation.
Justice department spokeswoman Sarah Isgur Flores called those reports “totally false”.
Either way, Republicans and Democrats vowed the House and Senate Intelligence Committees’ investigations into the Russia claims would continue.
Republican Senator Lindsey Graham said if President Trump believed replacing James Comey would halt the inquiries “he made a big mistake”.
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