On 12 March 2018, Martínez received his first call-up for the senior team for two friendly matches against Italy and Spain. He made his debut against the latter on 27 March, coming on as a substitute for Gonzalo Higuaín in a 6–1 defeat. In May 2018 he was named in Argentina’s preliminary squad for the 2018 FIFA World Cup in Russia but was omitted from the final selection. Later that year, he made his full debut in a 4–0 friendly win over Iraq during which he also scored his first senior international goal. In May 2019, Martínez was included in Lionel Scaloni’s final 23-man Argentina squad for the 2019 Copa América. In Argentina’s final group match against Qatar on 23 June, he scored the opening goal in a 2–0 win, which enabled them to advanced to the knock-out stages of the competition. On 28 June, in the quarter-finals of the tournament, Martínez scored the opening goal in an eventual 2–0 win over Venezuela with a back-heel in the opening ten minutes of the match; he was later named Man of the match, and the victory enabled Argentina to advance to the semi-finals of the competition. On 10 September 2019, Martínez scored his first international hat-trick in a friendly against Mexico, which Argentina won 4–0. On 28 June 2021, he scored Argentina’s final goal in a 4–1 win over Bolivia in his nation’s final group match of the 2021 Copa América. On 3 July, he scored the second goal in a 3–0 win over Ecuador in the quarter-finals of the competition. On 6 July, Martínez scored the opening goal in a 1–1 draw in the semi-finals against Colombia; he later netted his spot kick in Argentina’s eventual 3–2 penalty shoot-out victory to progress to the final.