Massú's mother Sonia Fried is of Jewish descent, his father Manuel Massú has Arab ancestry. Massú's enthusiasm for sport was sparked by his grandfather Ladislao Fried when Massú was five years old.
In 1997 Massú was one of the best young players in the world. He won the Orange Bowl , the junior tournament at Wimbledon and the junior tournament at the US Open . Also in 1997, Massú joined professional tennis.
In 2000, Massú qualified for the Olympic Games in Sydney and led the Chilean Olympic team as the flag bearer during the opening ceremony. But at the tennis tournament he was eliminated in the second round. In 2003 and 2004 he won the World Team Cup with his friend Fernando González .
He achieved his greatest successes at the 2004 Olympic Games in Athens. In doubles he and his partner Fernando González won the first ever Olympic gold for Chile. They defeated the Germans Nicolas Kiefer and Rainer Schüttler in a tight five-set game . A day later, Massú crowned his participation in the Olympics by winning the individual. In the final, he won against the American Mardy Fish in five sets with 6: 3, 3: 6, 2: 6, 6: 3 and 6: 4. In the following years he lost touch with the top and was often in the shadow of his compatriot Fernando González, who was much more successful at the time. In addition to the modest performances in the individual, many Davis Cup clashes were with moderate success, which always ended with an early elimination of Chile.
Massú fell far behind in the rankings, which made it difficult to participate in major tournaments. On July 28, 2008 he took part in the preparation for the Olympic Games in Beijing at a challenger tournament in Belo Horizonte and reached the final. He was the defending champion in Beijing and surprised many when he defeated the favored Belgian Steve Darcis 6: 4, 7: 5 in the first round . In the second round he had to admit defeat to the Argentine David Nalbandian 6: 7 0 and 1: 6.
On August 27, 2013, Massú announced his retirement from professional tennis. His best position in the ATP world rankings was 9th place, which he reached shortly after his Olympic victory.