Grigor Dimitrov, Borna Coric and Viktor Troicki all revealed they had coronavirus after playing at Djokovic's Adria Tour competition.
Djokovic, 33, played fellow Serb Troicki in the first event in Belgrade.
In a post on Twitter, Djokovic said it had been "too soon" to stage the tournament.
"I am so deeply sorry our tournament has caused harm," added Djokovic.
He said the tournament had been organised with "a pure heart", "good intentions" and a belief that they had "met all health protocols".
"We were wrong and it was too soon," Djokovic said.
The remaining Adria Tour events in Banja Luka and Sarajevo have now been cancelled Djokovic's brother Djordje, who is a director of the tournament, has confirmed.
"Unfortunately, due to all the events that happened in the last few days, we have decided that the most important thing right now is to stabilise the epidemiological situation, as well as for everyone to recover," he said.
Britain's Andy Murray said the positive tests were a "lesson for us", while Australian Nick Kyrgios called playing a "bone-headed decision".
A statement on Djokovic's website said: "Immediately upon his arrival in Belgrade [after the second event] Novak was tested along with all members of the family and the team with whom he was in Belgrade and Zadar. He is not showing any symptoms."