Puia earned 7 caps for the Italy national football team between 1962 and 1970, and was included in the Italian squad for the 1970 FIFA World Cup, although his only World Cup appearances came in the 1970 qualifying tournament; Italy reached the final of the competition, only to lose out to Brazil 4–1. He made his international debut on 11 November 1962 against Austria, whilst his final appearance came on 10 May 1970 against Portugal.