Graham, who had represented South Carolina in the US Senate since 2003, died on Saturday night, according to a statement issued by his office.
"Senator Graham's family appreciates prayers at this time and asks for privacy during this incredibly difficult period," the statement said.
Emergency response at Capitol Hill home
Emergency personnel responded to a reported cardiac arrest at Graham's Capitol Hill residence on Saturday night, according to police scanner audio cited by NBC News.
Photographs reviewed by NBC News showed paramedics carrying a person on a stretcher from the senator's home to a waiting ambulance, while police and fire crews were also present at the scene.
Key Republican voice in the Senate
Graham was serving as chairman of the Senate Budget Committee and was seeking a fifth six-year term in the November elections.
Over more than two decades in the Senate, he emerged as one of the Republican Party's most recognisable lawmakers and a leading voice on defence, national security and international affairs.
A longtime ally of President Donald Trump, Graham played a prominent role in shaping the party's positions on military and foreign policy issues.
Senator Lindsey Graham with US President Donald Trump. Photo: Wikimedia Commons
Had just returned from Ukraine
Graham had returned from Kyiv just a day before his death, where he met Ukrainian President Volodymyr Zelenskyy on Friday.
He had also been scheduled to appear on NBC News' Meet the Press on Sunday.
Death comes amid McConnell's hospitalisation
Graham's death comes as fellow Republican Senator Mitch McConnell continues to recover in hospital after suffering a cardiac emergency last month.
McConnell's office has confirmed that the former Senate Republican leader remains under medical care but has not released further details about his condition.