Labović made the Serbian national basketball team under head coach Moka Slavnić for the EuroBasket 2007.

During summer 2012, head coach Dušan Ivković included Labović on the preliminary list of players for the EuroBasket 2013 qualifying, but the 25-year-old power forward who had spent the preceding club season with BC Krasnye Krylia from Samara didn't make the final cut.

Stung by Ivković's comment, Labović responded months later, in September 2012, by putting out a bitter, somewhat cryptic, and highly unusual press release published by Serbian sports media outlets.

In the release, Labović criticizes 68-year-old Ivković's professional integrity and coaching skills, accusing the famous coach of letting his agent Miško Ražnatović of the BeoBasket agency exert an undue influence when it comes to squad selection for the national team.

That year, 2008, your team selection raised the transfer market price for a lot of players that never deserved it, while lowering mine considerably.

Ninety percent of the players that participated in that qualifying cycle soon made millions as a result of the exposure received through the national team.

I later did too, thank God, despite not being in the national team, despite being ignored by that managerial agency, and despite your phone calls around Europe to give instructions how players should play......

[20]A few weeks after his press release, Labović's club BC Nizhny Novgorod led by a Serbian head coach Zoran Lukić, reprimanded the player although his punishment was not specified.

[22] The incident occurred at a pool party in the Belgrade suburb of Ovča where reportedly inebriated Labović began smashing bottles and verbally menacing the property's owner, identified in the Serbian press reports as Lazar M., who eventually called the police.

After being kept for 12 hours at a Borča police station in order to sober up, Labović had a misdemeanour investigation request (prekršajna prijava) filed against him.

[22] Labović was arrested in the Belgrade suburb of Železnik on 7 December 2021 in the immediate aftermath of an incident that reportedly saw him assault a taxi driver and drive off with his vehicle.

[23] The altercation reportedly began when Labović—while getting into the said taxi—took issue with the driver's request for Labović to have a seat in the back of the car in accordance with COVID-19 epidemiological measures.