Max Sillig was the player-coach of the Swiss ice hockey team at the 1920 Antwerpen Olympics. Internationally he had also competed at the 1910 and 1911 European Championships and the LIHG Tournament in 1912 and 1913. He learned to played hockey while studying at Oxford University in the 1890s. Domestically he started playing in 1904 with Institut Sillig, which later became Bellerive HC, and played with that club through 1924, although he had brief stints with Les Avants HC (1906-08), Leysin SC (1907/08), and Lausanne CP (1908/09).
Sillig was President of the Ligue Internationale de Hockey sur Glace (LIHG) from 1920-22, after having been Vice-President in 1912-13. He was co-founder of the Swiss Ice Hockey Association and served as their President. Sillig was the director of a private school in Vevey, the Institut Sillig, succeeding his uncle Édouard and father Oscar in that position.