At 1.86 metres tall, Kašpárková started her professional athletics career as a high jumper and finished sixth at the 1988 World Junior Championships in Athletics. She won the bronze medal in the 1989 European Athletics Junior Championships, and she went on to participate in the women's high jump at the 1992 Barcelona Olympics for Czechoslovakia. Her last period as a high jumper also brought her best performance – she jumped a personal best of 1.95 m in Banská Bystrica in early 1993.