Burgnich began his career with local side Udinese, making his Serie A debut with the club on 2 June 1959, in a 7–0 away defeat to Milan. After short spells at the Friulian side, and subsequently Juventus (where he won the 1960–61 Serie A title), and Palermo, it was with Internazionale that he found his spiritual home in the 1960s, after being acquired in 1962.