Wibier started playing tennis at the age of nine. In 1983 he won the U12 double European championship alongside Richard Krajicek . In his youth he attended a tennis school supported by the Dutch Tennis Association, which trained Jacco Eltingh , Hendrik Jan Davids and Menno Oosting , among others . He became a professional tennis player in 1989 and earned his first world ranking points at satellite tournaments. In 1991 he was in the finals of the ATP Challenger tournaments in Hobart and Christchurch . Two years later he was at the side of Patrick Rafter in the final of the Challenger Tournament in Nagoya . His most successful year was 1994 when he along with his compatriot Stephen Noteboom the ATP tournament of Rosmalen won. This should remain his only tournament success on the ATP World Tour. By 1998 he reached three final rounds, including the International Series Gold tournament in Washington . In the course of his career, he was also able to win five double titles on the ATP Challenger Tour. He reached his highest ranking in the tennis world rankings in 1997 with position 126 in singles and 42 in doubles.
His best individual results in Grand Slam tournaments were qualifying for the Australian Open and Wimbledon , but here he was eliminated in the first round. In 1997 he reached the quarterfinals of the Australian Open alongside Stephen Noteboom. In mixed he appeared at the French Open , Wimbledon and the US Open , but could never advance to the second round.