Woods handed the ball to Julian Nexsen during his final round, after he made a bogey on the fifth hole.
The ball was put up for auction on 27 March – after a starting bid of $500, it fetched $64,124.40 (£51,626) when the auction closed on Sunday.
The tournament was Woods’ first major championship victory and made him the youngest player to win the Masters.
The victory set the tone for Woods’ record-breaking career. His four-day score was 270, 18 under par – breaking the previous record held by Jack Nicklaus.
“Unless Tiger himself or his caddie Fluff intentionally saved a ball from this historic final round [which we doubt], this may be the only confirmed golf ball from the final round of Tiger Woods’ first Major Championship victory,” the auction house said.
The auctioneers say dozens of people witnessed Woods give the ball to Mr Nexsen, including a reporter from the Washington Times.
“After making his first bogey in 36 holes yesterday, Woods stopped on his way to the sixth tee to give a ball to 9-year-old Julian Nexsen of Greenville, SC [South Carolina],” the paper reported.
The newspaper cutting, Mr Nexsen’s badge from the 1997 Masters Tournament, pairings sheets from the Sunday final round and the golf ball have been framed together ever since.
Mr Nexsen signed a legal declaration, certifying the authenticity of the golf ball and the story of that final round interaction with Woods.