The Bulgarian revealed the news on Instagram on Sunday, less than 24 hours after playing at the event against Borna Coric.
The final was due to be contested between world No 1 and tournament organiser Novak Djokovic and Andrey Rublev.
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A statement from the Adria Tour said: "As a precaution and to protect the health of all participants and visitors, the organisers of Adria Team have decided to cancel the grand finale of the tennis spectacle planned for tonight.
At all times we have strictly followed the epidemiological measures in place with the countries where the Adria Tour was organised. None of the people involved in the organisation and who have been in contact with Grigor have any symptoms. However, we are in close contact with health authorities to insure that all people who were in contact with Grigor Dimitrov will be tested tonight.
Dimitrov played the Adria Tour in Belgrade and Zadar, but returned home to Monaco after feeling unwell during his defeat to Coric.
He had close interactions with a number of players and played basketball with Djokovic, Alexander Zverev, Marin Cilic and others this weekend.
There is no indication of when he caught coronavirus.
The ATP Tour is set to resume on August 14 while the WTA Tour starts again on August 3.
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