Scalia was 79. The cause of death of the country's longest-serving justice was not immediately known.
He was a guest at the Cibolo Creek Ranch, a resort in the Big Bend region south of Marfa, and had arrived at the 30,000- acre ranch on Friday, according to a federal official. He had also attended a private party with about 40 people last night.
Someone at the ranch went in to check on him and found him unresponsive, CNN reported.
Calling the senior Justice as "larger than life" and a "brilliant legal mind", President Barack Obama paid tribute to Scalia and said he would honour his responsibility to fill the Supreme Court seat left vacant by his death.
In a statement, Chief Justice John Roberts said he and other justices were saddened to hear of Scalia's death.
Scalia's unexpected death triggered a political tussle over the successor as political leaders on both sides of the partisan divide staked out their positions in the fierce fight to come over the nomination of the next justice that could potentially tip the balance of the court from its current 5-4 conservative majority to a liberal one.
The president's comments followed those of Republicans who wasted little time - as news of Scalia's unexpected death spread - arguing that Obama should leave the choice to his successor.
"They're about the institution to which Justice Scalia dedicated his professional life, and making sure it continues to function as the beacon of justice that our Founders envisioned," he said in brief remarks.
The sudden death of the conservative icon has catapulted Indian-American judge Sri Srinivasan to the top of succession stakes amid intensified campaigning for the much-awaited presidential polls.
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An outspoken opponent of abortion, affirmative action and what he termed the "so-called homosexual agenda", Scalia's intellectual rigour, flamboyant style and eagerness to debate his detractors energised conservative law students, professors and intellectuals who felt outnumbered by liberals in their chosen professions.
"He was the solid rock who turned away so many attempts to depart from and distort the Constitution," Abbott said.
According to US Marshals Service spokesperson Donna Sellers, Scalia left the party and retired to bed earlier than others but when he did not join all for breakfast, a person involved with the ranch went to his room, where he discovered his body.
A priest was called to administer last rites.
A federal official, who asked not to be named, said there was no evidence of foul play and it appeared that Scalia died of natural cause.
Reaction and condolences quickly poured in from politicians and presidential hopefuls. President George H W Bush, who was vice president when Scalia was appointed to the court, called him one of Reagan's "many enduring legacies to the United States."
"Both his admirers and his detractors agreed that Justice Scalia was one of the sharpest constitutional intellects to ever serve on the bench," Bush said in a statement.
"I considered him a personal hero, and Barbara and I were honored to call him a friend... His death is a great loss for us all," Bush said.
"The totally unexpected loss of Supreme Court Justice Antonin Scalia is a massive setback for the Conservative movement and our country!" Trump tweeted.
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