The top-ranked Serb is the fourth player to test positive for the virus after playing last week in Belgrade and last weekend in Zadar, Croatia. His wife also tested positive.
"The moment we arrived in Belgrade we went to be tested. My result is positive, just as Jelena's, while the results of our children are negative," Djokovic said in a statement.
Djokovic has been criticized for organizing the tournament and bringing in players from other countries.
Viktor Troicki said Tuesday that he and his pregnant wife have both been diagnosed with the virus.
Grigor Dimitrov, a three-time Grand Slam semifinalist from Bulgaria, said Sunday he tested positive for the virus. Borna Coric played Dimitrov on Saturday in Zadar and said Monday he has also tested positive.