Şükür won his first cap for Turkey in a friendly with Luxembourg in March 1992 – his debut being awarded by German manager Sepp Piontek – scoring his first international goal in his next match, against Denmark, and totalling six in his first 11 appearances. He netted seven in qualification for UEFA Euro 1996 and started all of the matches at the finals in England, in which they were eliminated in the group stage without scoring a single goal.