Vašek won the Czech U18 junior title in 1990 by beating Martin Damm in the final and became a professional tennis player in the same year. He achieved a first respectable success in 1991 in Copenhagen on the side of Cyril Suk by reaching the semi-finals of the doubles competition. Success on the ATP World Tour remained the exception, however, and most of Vašek's career took place on the ATP Challenger Tour . Here he was successful in both singles and doubles and won four singles and eight doubles titles between 1993 and 2001. Once in his career he was in an ATP final, in Jakarta in 1995 he was defeated by Paul Haarhuis in two close sets. He reached the highest ranking in the tennis world rankings in 1995 with position 91 in singles and in 1999 with position 168 in doubles.