Djokovic -- the No. 1 men's player -- was set to face Andrey Rublev in the tournament final Sunday in Zadar.
"We are very sorry and we tried to comply with all prescribed epidemiological measures," said Djokovic's brother Djordje, the director of the Adria Tour.
"At this time, we are in contact with all health services so that as many people as possible who have been in close contact with Grigor will be tested immediately [Sunday].
"None of the people involved in the organization and who have been in contact with Grigor have symptoms. We do not want to put anyone in danger and the final match has been canceled."
Dimitrov revealed his positive test Sunday on Instagram. He said he got the result in Monaco. Dimitrov, 29, played alongside Djokovic, No. 3 Dominic Thiem and No. 7 Alexander Zverev last week when the Adria Tour was in Belgrade, Serbia.
He also lost to No. 33 Borna Coric Saturday in Zadar before he withdrew from the tournament. Dimitrov cited "physical effort and exposure to the sun" for the initial reason of his exit.
"I want to make sure anyone who has been in contact with me during these past days gets tested and takes the necessary precautions," Dimitrov wrote Sunday. "I am so sorry for any harm I might have caused. I am back home now and recovering. Thanks for your support and please stay safe and healthy."
The Adria Tour also featured No. 37 Marin Cilic, No. 157 Danilo Petrovic, No. 246 Pedja Krstin and No. 299 Nino Serdarusic. Tournament organizers recommended 14 days of self isolation for anyone who was in close contact with Dimitrov for more than 10 minutes.
Dimitrov was in contact with Thiem in Belgrade but Thiem has since tested negative for the coronavirus. Thiem played in the Ultimate Tennis Showdown Saturday at the Mouratoglou Academy in Biot, France.
The ATP Tour and WTA Tour remain suspended but are scheduled to resume in August after a nearly five-month hiatus.