Sušić began his career with the football club Krivaja in his hometown Zavidović and later he was transferred to FK Sarajevo, where he was to become a legendary figure by the late 1970s. During the 1979–80 season, he was top scorer in the Yugoslav First League with 17 goals. In 1979, he was honoured as the Yugoslav Footballer of the Year, also being selected as the best athlete coming from the Republic of Bosnia and Herzegovina.
In 1982, Sušić signed with Paris Saint-Germain, where he became a star. Hardly ever injured, he performed at a high level well past his 30s. The Yugoslav international was never injured nor suspended, thus allowing him to score 96 goals and make a record 61 assists for PSG between 1982 and 1991. At 36, Sušić left the capital for a final year with Red Star Saint-Ouen.
During a 13-year span, Sušić appeared 54 times with the Yugoslav national team, netting 21 goals, in spite of the fact that he was always in the role of midfield playmaker. He represented the nation at the 1982 and 1990 World Cups, and at Euro 1984. On 19 June 1990, Sušić opened the score in Yugoslavia’s 4–1 World Cup win against the United Arab Emirates, aged 35.
In 2004, to celebrate UEFA’s Jubilee, he was selected as the Golden Player of Bosnia and Herzegovina by the Football Association of Bosnia and Herzegovina as their most outstanding player of the past 50 years.
When he retired Sušić coached Cannes and from 2003-2004 he managed İstanbulspor and Konyaspor.
On 28 December 2009, Sušić was named coach of the Bosnia and Herzegovina national football team. His debut was a friendly match against Ghana in Sarajevo. Bosnia and Herzegovina won the game 2–1 after goals from Vedad Ibišević and Miralem Pjanić.
As of 11 November 2011, Sušić’s Bosnia national football side was on a seven game unbeaten streak run. BiH football team, together with Safet Sušić is on the good path to qualify for 2014 World Cup which will be held in Brazil.