[2][3] On 5 October 2020, Martínez Quarta signed a five-year contract with Serie A club Fiorentina.

[5][better source needed] On 26 October 2023, he netted his first goal in European competitions and provided an assist in a 6–0 victory over Čukarički in the Europa Conference League.

[7] On 7 January 2025, Martínez Quarta returned to River Plate, departing Fiorentina after four-and-a-half seasons.

[8] On 5 September 2019, Martínez Quarta debuted for the Argentina national team in a friendly 0–0 draw against Chile, playing the full 90 minutes.

[9] In June 2024, Martínez Quarta was included in Lionel Scaloni's final 26-man Argentina squad for the 2024 Copa América.