The sources said discussions have been under way for months between the panel and Mr Trump Jr regarding his possible testimony.
It's the first known subpoena of a member of Trump's immediate family and a new sign that the Senate panel is continuing with its own two-year-long investigation.
The abrupt disclosure this week of the Trump Jr. subpoena - issued at least a week ago, according to people familiar with the situation - came shortly after Senate Majority Leader Mitch McConnell, R-Ky., insisted that he considered as closed all matters investigated by special counsel Robert Mueller III.
The subpoena for Trump Jr.'s testimony marks an escalation of the Senate Intelligence Committee's probe into Russian election interference. "I think he'd rather not ever be involved", Trump said.
Committee sources would not confirm the subpoena or what they want to discuss with the president's eldest son, who now helps run the Trump Organization, the family's real estate empire, and helps his father re-election campaign. "Yeah, I'm pretty surprised".
Mueller's team of prosecutors said there was a "reasonable argument" that Trump Jr. had violated campaign finance laws but concluded they did not believe they could obtain a conviction.
But Mueller's report states that the chief handler of the project, Trump's now-jailed personal lawyer Michael Cohen, briefed Trump Jr about the project "on multiple occasions".
Trump, who has blasted the investigations into him and Russian Federation, defended his son, who runs the Trump Organization - a private business that the Republican president still owns.
Trump last week said that it was Barr's call, but later declared on Twitter that Mueller should not testify.
But Senator John Cornyn sounded unenthusiastic about hauling Trump Jr in for more questioning.
"We have a 400-plus page report that was determined after about $30 million of money spent, dozens of investigators, hundreds of subpoenas and inquisitions that there was no underlying crime and no obstruction", Tillis said. "And I think we have an important job to do to try to keep the Intelligence Committee out of politics".
While McConnell said in his Tuesday speech that it was "case closed" on the Mueller probe, his office noted that he didn't go so far to say the intelligence panel's work was done.