Born in Antwerp to Serbian parents, Mile Svilar is the son of the former Antwerp and Yugoslavia goalkeeper Ratko Svilar. He was formed at KFCO Wilrijk and Beerschot before joining Anderlecht's academy in 2010, signing his first professional contract with the Brussels club on his eighteenth birthday in 2015.

Svilar moved to Benfica in August 2017 on a five-year contract, a transfer that led to a compensation dispute between the two clubs. He made his competitive debut against Olhanense in October 2017 and, later that month, became the youngest goalkeeper ever to appear in the UEFA Champions League, breaking a record previously held by Iker Casillas. Ahead of Odysseas Vlachodimos in the pecking order only briefly, he spent the bulk of his Lisbon years as a reserve and with Benfica B in the Segunda Liga.

His contract expired at the end of the 2021/22 campaign and he was not retained. On 1 July 2022 he joined Roma on a free transfer, signing until June 2027, and subsequently established himself as a first-choice goalkeeper in Serie A. He represents Serbia at international level.