Zelenka was born into a Jewish family. He worked as a Czech architect, graphic artist, stage and costume designer. Between 1929 and 1933 he worked for the famous Osvobozené divadlo (Liberated Theatre or Prague Free Theatre) of Czech avant-garde artists of the group Devětsil. In Prague he built several houses in the international style. He knew that his family was in danger after Nazi-Germany occupied Czechoslovakia and was prepared to leave to the UK. In the end, he decided not to flee, because his son got ill. On July 13, 1943, he was deported with his family to the Terezín Ghetto and in October 1944. In Terezín he worked as the set designer of the famous children's opera Brundibár, performed all over the world these days. Zelenka died during a transport from Terezín to the concentration camp Auschwitz/Oświęcim, Poland. Neither his wife nor his son survived the war.
One of his posters he designed for the Osvobozené divadlo.