When he retired, the reigning Australian Open singles champion was trailing Nikolay Davydenko 4-6, 3-6, 6-4.
"I decided to stop because I don't want to risk my health," Djokovic told the BBC. "I tried to play but in the end I was aware of the fact that I am very dizzy and I have a lack of energy."
The symptoms also forced him to miss Friday's scheduled match against Mikhail Youzhny and Saturday's doubles. It made the match between Serbia's Viktor Troicki and Russia's Dmitry Tursunov meaningless.
In April's quarterfinals, the Russians will face the Czech Republic, a 3-2 winner against Belgium.
Russia lost last year's Davis Cup final 4-1 to the United States.
In other matchups, it was: Germany 3-2 over Korea, United States 4-1 over Austria, France 5-0 over Romania, Argentina 4-1 over England, Peru 3-0 over Spain and Sweden 3-2 over Israel,