Kukoč was on the junior Yugoslavian Under-19 national team that won the 1987 FIBA Under-19 World Cup, where he was named the tournament MVP. He was also on the senior men's Yugoslavian national team that got the silver medal at the 1988 Summer Olympic Games. He was named the MVP of the 1990 FIBA World Championship, where he also won a gold medal. With Yugoslavia, he also won the gold medal at the EuroBasket 1989 and the EuroBasket 1991. He was also named the MVP of the 1991 EuroBasket tournament.