Internationally, he played for FR Yugoslavia national team in the qualification for the 1998 FIFA World Cup, although he was not selected to the country's squad for the final tournament.
Drobnjak later attributed his early development to "Špaco" Poklepović: "I was a kid back then and in one workout, shooting [the ball], I hit him in the head, but he didn't get upset.
"[1]Drobnjak joined Red Star Belgrade ahead of the 1992–93 season, after which he was the league's top scorer along with Vojvodina's Vesko Mihajlović.
[2] Amidst international sanctions against Yugoslavia, Drobnjak asked Red Star's sports director Dragan Džajić if there was any opportunity could leave both the club and country.
[3] In 1997, Drobnjak switched to fellow French club Lens, helping them win the league in his debut season under coach Daniel Leclercq.
He made his debut on 6 October 1996 in a 8–1 away win against Faroe Islands under coach Slobodan Santrač during the 1998 FIFA World Cup qualification.