Berdych dropped out after losing Thursday's Sony Open quarter-final against Frenchman Richard Gasquet 6-3 6-3 in Miami.
"Last night's match was the last straw for me," he told the Czech Davis Cup Facebook page.
"I woke up this morning and my shoulder hurt so much that it was clear I would not be able to play in Kazakhstan."
The Czech team will now be Radek Stepanek, Lukas Rosol, Jan Hajek and Ivo Minar.
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