A native of Holešov, Vodička began competing on tour in the 1930s.

He played a Davis Cup tie for Czechoslovakia against Yugoslavia in Prague in 1946, as the teammate of Jaroslav Drobný.

In 1948, aged 40, he made the singles fourth round of the French Championships.

Along the way he had a win over Alejo Russell, after coming back from dropping the first two sets 0–6.

[4] His nephew Leo Marian Vodička is a noted operatic tenor.