Giannouzakos was a member of the senior men's Greek national basketball team. With Greece's senior men's national team, he had 147 caps, and he scored 956 points (6.5 points per game). With Greece's senior men's team, he played at the 1972 Pre-Olympic Tournament, the EuroBasket 1973, the EuroBasket 1975, and the EuroBasket 1979.