Born in Buenos Aires, Wolff is the son of Waldo Ezequiel Wolff, who was also a professional goalkeeper for clubs including Ituzaingó in Argentina and Maccabi Kiryat Gat in Israel. The elder Wolff later became a politician.[2] Marco Wolff began playing football in Sociedad Hebraica Argentina, and represented his nation at the 2013 Maccabiah Games.[1]
Wolff began his professional career at Tigre. He made his only appearance for the club on 10 March 2020 in a 2–0 loss away to Club Bolívar of Bolivia in the second game of the group stage of the Copa Libertadores. The game was played at 3,500 metres above sea level in La Paz, and Tigre fielded several fringe players due to focus on the domestic league.[3][4]
In July 2021, Wolff transferred to Maccabi Petah Tikva in the Israeli Premier League on a one-year deal with the option of two more.[5] He cited the COVID-19 pandemic in Argentina and his homeland's economic crisis as reasons for his emigration.[2] Wolff, who is Jewish, qualifies for Israeli citizenship under the Law of Return and therefore does not take up a place in the league's quota of foreign players.[6]
Wolff's team were relegated in his first season, but returned to the top flight as champions of the 2022–23 Liga Leumit. The title was sealed with a 7–0 win at Bnei Yehuda Tel Aviv on 1 May. Wolff said that he communicated with his teammates mainly in English, having a rudimentary knowledge of Hebrew.[7]
On 30 May 2024, Wolff won his second title with the club, Israel State Cup, after beating Hapoel Be'er Sheva 1–0 in the final.[8] He then signed a new contract until 2027.[9]