Šrejber studied electrical engineering at Charles University in Prague , but at the age of 19 he decided to pursue a career as a professional tennis player. In 1985 he won his first Challenger tournament in Neu-Ulm , the following year he qualified as a qualifier in the final of the ATP tournament in Toronto , but lost to Joakim Nyström there . In 1988 he won his first doubles tournament on the ATP World Tour at the side of Petr Korda , as well as his only single title at the tournament in Rye Brook. He achieved his highest ranking in the tennis world rankings in 1986 with position 23 in singles and in 1989 with position 37 in doubles.
His best individual result in a Grand Slam tournament was reaching the quarter-finals at the 1986 US Open . In 1990, he was in the quarter-finals of the French Open in the doubles competition . He was also in the round of 16 of the Australian Open in 1987 .
Šrejber played 14 singles and five doubles games for the Czechoslovak Davis Cup team between 1986 and 1991 . His greatest success with the team was reaching the semi-finals of the world group in 1986, where he was able to win his two singles against Bruno Orešar and Slobodan Živojinović in the quarter-finals against Yugoslavia . In the 1-4 semi-final defeat against Sweden he lost both singles. At the 1988 Summer Olympics in Seoul , he competed for Czechoslovakia in singles and doubles. While he failed in the singles in the first round against the Italian Paolo Canè , he won the bronze medal in doubles on the side of Miloslav Mečíř .