He was named the 2000 IHF World Player of the Year.

[1] He was included in the European Handball Federation Hall of Fame in 2023.

[2] Over the course of his career that spanned over two decades, Škrbić played for Jugović, Crvena zvezda (1988–1993), Atlético Madrid (1993–1994), Alzira (1994–1995), Ademar León (1995–1997), VfL Hameln (1997–1998), Celje (1998–2000), HSG Nordhorn (2000–2002) and Barcelona (2002–2007).

He won the EHF Champions League with Barcelona in the 2004–05 season.

At international level, Škrbić represented FR Yugoslavia in eight major tournaments, winning two bronze medals at the World Championships (1999[3] and 2001[4]) and one bronze at the European Championships (1996).