Madrid had gone into quarantine after a player on their basketball team tested positive for the virus, which now has almost 18,000 confirmed cases in Spain.
Jovic was expected to observe 28 days of self-isolation in Serbia but was reportedly spotted outside of his apartment.
The 22-year-old addressed the issue in a post on his Instagram page, saying he was of the understanding he could still visit a pharmacy - as he had been able to in Madrid.
"Since the situation in the world and in our country is very difficult, I have to come forward and give support to my people," Jovic wrote.
"First of all, I am very sorry that I am the main topic these days and that I am constantly being written about, not the heroes of this crisis, doctors and all the medical professionals.
"While in Spain, I [tested] negative for coronavirus and decided to come to Serbia to help and support our people and be close to my family, in agreement with the officials.
"When I landed in Serbia, I was once again tested and coronavirus negative.
"It is very unfortunate for me that some people did their job unprofessionally and did not give me the correct instructions for how to behave in self-isolation.
"In Spain, I was allowed to go to a pharmacy and a supermarket so that I could get the groceries I needed, which is not the case here.
"I apologise to all the people if I compromised them in some way and I hope that we can manage to get through all this together.
"Support Serbia and let's stick together."
Ascoli winger Nikola Ninkovic also reportedly breached protocol, and Serbian president Aleksandar Vucic vowed in a news conference that repeat offences would prompt arrests.
"These young men are millionaires, so they think they can do everything - you can't do everything," Vucic said.
He added: "Everyone will be severely punished, all who disobey the law. The easiest thing to do is punish them.
"I'm sure those two boys who have mentioned remorse have been reported, and I hope we can avoid it. They are both in isolation, and if they try to get out, they will be arrested.
"They are basically good guys, I understand them. We have many who should be more responsible and have not gone into isolation."