Budućnost Drobnjak joined
Budućnost ahead of the
1987–88 season. He made his professional debut under coach
Stanko "Špaco" Poklepović, during a time when Budućnost fielded their most accomplished generation at the time; Drobnjak's teammates at Budućnost included
Dragoje Leković,
Branko Brnović,
Željko Petrović,
Predrag Mijatović, and
Dejan Savićević. Drobnjak later attributed his early development to "Špaco" Poklepović:
Red Star Belgrade 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. On 15 May 1993, he scored the winning goal in the
final of the 1993 Yugoslav Cup, in which Red Star beat
Partizan 1–0. He was Red Star's top scorer in the
1993–94 season along with teammate
Ilija Ivić, and was fifth highest goal scorer in the league that season. Under coach
Frédéric Antonetti, he spent the following three seasons at the club, scoring 50 goals in 100 league games. He was the
fourth highest goal scorer in the league that season.
Later career He subsequently moved to Japan and played for
Gamba Osaka. After a year, Drobnjak returned to France and joined
Sochaux. He also spent one season at
Martigues, before retiring in 2002. ==International career==