After playing his first Grand Prix event in 1970, Amritraj achieved his first significant success in singles in 1973 when he reached the quarterfinals at two Grand Slam events. At Wimbledon, he lost in five sets to the eventual champion Jan Kodeš and later that summer at the US Open, lost to Ken Rosewall after having beaten Rod Laver two rounds earlier.

Amritraj beat Björn Borg in the second round in the US Open in 1974 before losing to Rosewall in quarterfinals. In 1979, he lost in the second round of Wimbledon to defending champion Borg after being up two sets to one and leading 4–1 in the fourth set. He reached his career-high ranking in singles of world No. 16 in July 1980. In 1981, he reached the quarterfinals of Wimbledon before losing in five sets to Jimmy Connors after being up 2–0. He beat John McEnroe in the first round of Cincinnati Masters in 1984. Overall, he had five career wins over Jimmy Connors in their eleven matches.

Amritraj was part of the India Davis Cup team that reached the finals in 1974 and 1987. Amritraj had a career singles win-loss record 384–296, winning 16 singles and 13 doubles titles.

Amritraj also had a brief acting career. His most notable appearance is probably as the MI6 intelligence operative Vijay in the 1983 James Bond film Octopussy. He also appeared briefly in Star Trek IV: The Voyage Home (1986) as a starship captain.

His son Prakash and nephew Stephen Amritraj are also professional tennis players. On 9 February 2001, Vijay was appointed a United Nations ambassador for peace. He has been raising awareness on the issues of drugs and HIV/AIDS and has raised funds to fight the spread of AIDS worldwide. Vijay Amritraj founded The Vijay Amritraj Foundation in 2006.