Djokovic was forced to retire with a muscle injury in the semifinal in Australian Open against Alexander Zverev and now says that he will not regain fitness in time for the clash against Denmark.
"I will not play the Davis Cup, and the tournament in Doha in a few weeks is also still uncertain", Djokovic told the Serbian press.
The Davis Cup match between Denmark and Serbia is scheduled to take place at the Royal Arena in Copenhagen from 31 January to 1 February.
In addition to Djokovic, Serbia have selected three players from the top-100. These are Miomir Kecmanovic (number 51), Dusan Lajovic (80) and Hamad Medjedovic (98).
In addition to Rune, Denmark will field Elmer Møller (160) and August Holmgren (199) in men's singles.
Two singles are to be played on Friday in Copenhagen, while a double and two singles are to be played on Saturday. Djokovic retired on Friday after losing the first set against Alexander Zverev. He was already suffering with an injury in the quarter-finals when he beat Carlos Alcaraz.