Viktor Troicki will replace Djokovic, who returned to Serbia on Thursday after beating Rafael Nadal on Monday in the U.S. Open final.
The top-ranked Djokovic also pulled out of Serbia’s opening match of the semifinals last year against the Czech Republic because he needed rest after the U.S. Open. He later led Serbia to its first Davis Cup title.
In Friday’s other singles match, Janko Tipsarevic will face Juan Martin del Potro.