Djokovic, who was set to represent Serbia in their January 31 - February 2 meeting with Denmark in Copenhagen, retired due to a hamstring injury in his Australian Open semi-final match against Alexander Zverev last week.
The 24-time Grand Slam champion was booed by the crowd at Melbourne Park and he responded by posting a photo of an MRI taken of his left hamstring with the caption: "Thought I'd leave this here for all the sports injury 'experts' out there."
Djokovic was part of the Serbian team which lifted the Davis Cup in 2010 following a memorable victory over France in Belgrade.
"We are weakened by not playing Novak, but we are still going for the win. The Danes have a great player in Holger Rune, but our players are also great and I believe in my team," Serbia captain Viktor Troicki said.