WASHINGTON—The Republican-led Senate Intelligence Committee in recent weeks subpoenaed Donald Trump Jr., the president’s eldest son, to testify about answers he gave congressional investigators as part of their Russia probe, according to people with knowledge of the matter, marking the first time a congressional panel has subpoenaed a member of President Trump’s family.

The subpoena—news of which came a day after Senate Majority Leader Mitch McConnell (R., Ky.) declared the Russia investigation “case closed”—is likely to further escalate tensions between the White House and Congress over Capitol Hill’s oversight efforts.

What the Senate committee wants to question Mr. Trump Jr. about is unknown.

In December 2017, the younger Mr. Trump testified privately before the committee for more than nine hours. He also spoke privately to the Senate Judiciary Committee in September 2017. The Judiciary Committee released a transcript of that interview, in which Mr. Trump was asked about efforts to build a Trump Tower in Moscow during the 2016 election and about a June 2016 meeting he arranged at Trump Tower in Manhattan between top campaign aides and a Russian lawyer linked to the Kremlin.

Prior to issuing the subpoena, the committee had asked Mr. Trump Jr. to voluntarily answer more questions, according to two of the people familiar with the matter. Mr. Trump Jr. offered to cooperate in writing but rebuffed the request to return in person, the people said.