Grün made his international debut against Yugoslavia on 13 June 1984, scoring on his debut. He is most famous in his home country for scoring the away goal that qualified Belgium at the expense of their neighbours Netherlands in the 1986 World Cup qualifying rounds. Belgium would go on to a very respectable fourth-place finish. He played in three FIFA World Cups for the Belgium national football team (1986, 1990 and 1994). He made his World Cup debut against Mexico on 3 June 1986. Grün is the sixth most capped player for Belgium with 77 caps. On the club level, he played for Anderlecht, Parma and Reggiana.
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