On 2 October 2019, Martínez scored his first goal in UEFA Champions League in a 2–1 away defeat to Barcelona in group stage; he became the first player since Roberto Boninsegna in 1970 to score at Camp Nou for Inter. Later in the competition, by scoring a brace in a 3–1 away win against Slavia Prague, Martínez reached two milestones: he became only the fourth Inter player (after Hernán Crespo in 2002, Christian Vieri in 2003 and Samuel Eto'o in 2010) and the fifth Argentinian player (after Hernan Crespo in 2002, Lionel Messi in six occasions, Sergio Agüero in 2019 and Ezequiel Lavezzi in 2013) to score in four consecutive Champions League games. On 17 August 2020, Martínez scored a brace in a 5–0 win against Shakhtar Donetsk to reach the 2020 UEFA Europa League Final.