Prpić was Yugoslav youth champion in 1980 . He became a professional tennis player in 1984 and was able to win two tournaments in the ATP satellite series in the same year and thus collect his first world ranking points. The following year he was in the semifinals of the Challenger tournament in Marrakech , he also reached the quarterfinals of the ATP tournaments in Bologna , Båstad and Palermo . During an encounter against Aaron Krickstein at the Miami Masters in February 1986, he suffered a serious knee injury, after which he was sidelined for approximately two years. During this time, a continuation of his professional career was extremely uncertain, which is why he enrolled at the University of Zagreb as a student of economics . He only started again in 1988, always wearing an extensive knee brace.
After his comeback, he stood at Rolf Hertzog's side in the double-finals of the Challenger tournaments in Munich and Münster . The following year he was in the final of the ATP tournament in Stuttgart , but lost to Martín Jaite . He also won the Agadir Challenger tournament . In 1990 he celebrated his only single title on the ATP World Tour after beating Goran Ivanišević in the final in Umag . In the same year he won his only ATP double title in Sanremo at the side of Mihnea-Ion Nastase . He reached his highest ranking in the tennis world rankings in 1991 with position 16 in singles and position 75 in doubles.
His best individual results in Grand Slam tournaments were quarter-finals at the Australian Open and the French Open . His best result in the doubles competition was a round of 16 at the 1992 Australian Open.
Prpić played from 1985 to 1986 and between 1988 and 1991 for the Yugoslav Davis Cup team . In 1993 he competed for Croatia. He had a total of 18 singles and ten doubles games. His greatest success with the team was participation in the semi-finals of the world group in 1988 and 1989. In the 0-5 defeat against Germany , he lost both singles against Eric Jelen and Boris Becker . In the 1-4 defeat against Sweden in the following year he again lost both singles against Mats Wilander and Jonas Svensson , but was able to win the doubles on the side of Goran Ivanišević. At the 1992 Summer Olympics in Barcelona he competed in singles and doubles for Croatia. In singles he reached the second round after defeating the Dane Kenneth Carlsen , in which he was defeated by Andrei Cherkassov . At the side of Goran Ivanišević, he won the bronze medal in men's doubles after losing in the semifinals to Wayne Ferreira and Piet Norval from South Africa .