[12] A midfielder with good technique, Petković started playing football in Ilidža as an eleven-year-old before joining the youth sector of his hometown side FK Sarajevo as a fifteen-year-old.

Petković emigrated from Yugoslavia in 1987, leaving FK Sarajevo and moving permanently to Switzerland, where he joined second division club Chur 97.

Sion achieved a third-place finish in the Nationalliga but Petković left the club at the end of the season after only making six league appearances.

After leaving Sion, Petković moved back into the lower tiers, first joining Martigny-Sports before returning to his first Swiss club, Chur 97.

On 23 December 2013, it was announced that Petković was to succeed Ottmar Hitzfeld as the manager of the Switzerland national team after the 2014 FIFA World Cup.

Petković was sacked as Lazio manager on 4 January 2014 and was replaced by Edy Reja, which resulted in a legal dispute concerning the contract termination.

At the UEFA Euro 2020, he led Switzerland to defeat world champions France 5–4 on penalties in the Round of 16, after a 3–3 draw, to qualify to the quarter-finals of the European Championship for the first time in their history.

[23] While living in Switzerland, Petković worked for Caritas Ticino, a Catholic relief development and social service organisation, for five years.