Navrátil celebrated his first major success on the ATP World Tour when he reached the round of 16 in Kitzbühel in 1981 , defeating Juan Aguilera . In the following years he could not repeat this individual success, only in 1984 he achieved a noteworthy result with the quarter-finals at the Swedish Open . In the same year he was again in the round of 16 in Kitzbühel and in the quarter-finals in Toulouse . His greatest success was taking part in the semi-finals in Prague in 1987, when he defeated Miloslav Mečíř in the first round and was ultimately defeated by Tomáš Šmíd .
Navrátil was more successful in doubles. In the course of his career he was able to win two titles on the ATP World Tour and two more on the ATP Challenger Tour . He reached his highest ranking in the tennis world rankings in 1987 with position 64 in singles and position 31 in doubles.
Navrátil was appointed to the Czechoslovak Davis Cup team once in 1983 . In the game against Paraguay he was used in the last individual, when the victory of the Czechoslovaks was already certain. He won his game against Víctor Caballero clearly in straight sets. After the end of his playing career, he became the captain of the Czech Davis Cup team.