After starting out at his hometown club Borac Banja Luka, Bojinović spent four seasons with Partizan (1995–1999) and won two trophies, before moving to Spain.

He played for three Liga ASOBAL teams, namely Ademar León (1999–2000), Bidasoa (2000–2001), and Barcelona (2001–2002).

In 2002, Bojinović moved to France and stayed with Montpellier over the next decade, winning nine national championships.

In 2012, Bojinović signed with Paris Saint-Germain, helping them win their first ever national championship in the 2012–13 season.

Bojinović made his major international debut for FR Yugoslavia (later known as Serbia and Montenegro) at the 2001 World Championship, winning the bronze medal.