Berdych announced his decision on Friday following his 6-3 6-3 Miami Masters quarter-final loss to Richard Gasquet, of France.
"I woke up this morning and I quickly felt a deep pain in my shoulder. It was clear that I wouldn't be able to play next week in Kazakhstan," he said.
The Czech Republic, the defending champions, will be now represented by Radek Stepanek, the world number 43, Lukas Rosol (64), Jan Hajek (98) and Ivo Minar (245), who steps in for Berdych.
Last November, Berdych and Stepanek led the Czech Republic to their first Davis Cup trophy since the country became independent a decade ago, beating five-time champions Spain 3-2 in the final.