Montiel began his professional career with River Plate in 2016, playing 140 games and winning honours including the Argentine Primera División in 2021 and the Copa Libertadores in 2018.

Born in González Catán, Buenos Aires Province, Montiel was a product of the Club Atlético River Plate academy.

[8] Playing five matches in the Copa Argentina, the team were eliminated on penalties in the semi-finals against Club de Gimnasia y Esgrima La Plata.

For the second season in a row, Montiel reached the Copa Libertadores final after twelve matches; however, River Plate would be defeated by CR Flamengo.

[9] On 20 February 2021, Montiel scored his first league goal for River, a penalty in a 3–0 win against Rosario Central in the first game at the Estadio Monumental after a six-month renovation.

[11] He made his debut on 14 September in a UEFA Champions League group stage 1–1 home draw against FC Red Bull Salzburg, replacing Navas for the last three minutes.

[12] Eight days later, he made his league bow by starting against Valencia CF at the Ramón Sánchez Pizjuán Stadium, scoring in the 15th minute of a 3–1 win before making way for Navas before the hour.

[15] On 23 August 2023, Montiel signed for Premier League club Nottingham Forest on a season-long loan with the option to make the move permanent.

[16][17] After one season in the Premier League, Montiel returned to Sevilla after completing his loan spell for Nottingham Forest after playing 802 minutes for the English team.

Forest had shown interest in signing him permanently, as well as fellow English side Everton FC and the Dutch team Feyenoord, but ultimately Montiel returned to Spain.