The player did so with the blessing of the club, and he maintains he tested negative for coronavirus.
Real Madrid have yet to comment on the matter.
Real Madrid forward Luka Jovic has angered the club after he ignored Serbia's self-isolation rules to fly home recently and, as a result, Los Blancos are said to be ready to offer him to Chelsea and Tottenham.
This sentiment was echoed by the country's Interior Minister Nebojsa Stefanovic, who stressed that Jovic's wealth and fame will not protect him from the weight of the law should he continue to break the quarantine rules in place.
Jovic, 22, has been the subject of fierce criticism in Serbia after flying home last Thursday, with the permission of Real Madrid's medical department.
"While in Spain, I tested negative for coronavirus, and I made a decision to travel to Serbia to help and support our people and be close to my family, in agreement with my club", Jovic wrote on Thursday.
"I am very sorry that some people have not professionally fulfilled their work and have not given me specific instructions on how I should behave during my isolation".
"When I arrived in Serbia, they gave me the test and it came out negative", Jovic explained, according to a separate Marca report.
Sources have said that Jovic's Real Madrid teammates are not impressed by these latest reports either. I apologise to everyone if, in any way, I have hurt or endangered someone.
"In the country I come from, and even in Italy, as far as we can see on the internet, anyone quarantined can go out to throw their trash once a day, go to a pharmacy or shop".
"The fact that they are known sportsmen, and that they are rich, will not stop them from being punished".
Spain has been particularly hard hit by the pandemic, which has caused the virtual lockdown of the entire country, with more than 17,000 cases and 767 deaths.
But Jovic is understood to be among a number of Serbian players playing overseas who have been criticised by the country's politicians for returning to the country in the last few days.
On Wednesday, there were 13,716 cases in Spain.