Buendía's senior career began at Getafe with whom he spent four years, including a short spell with Spanish club Cultural Leonesa, before he moved to England, joining Norwich City in 2018 and Aston Villa in 2021.

[citation needed] On 30 March 2014, still a junior, he made his senior debut, starting for the reserves in a 2–1 away win against Puerta Bonita in the Segunda División B.

[citation needed] On 5 July 2016, despite suffering relegation with Getafe at the end of the 2015–16 La Liga season, Buendía signed a new five-year contract with the club.

[17] Norwich would lose their next match to West Ham, a result which confirmed their relegation back to the Championship after only a single season in the top flight.

[21][22] On 29 April, following a campaign in which Buendía scored 15 league goals and added a further 16 assists, he won the EFL Championship Player of the Season award.

[24] On 7 June 2021, it was announced that an agreement had been reached for Buendía to be transferred to fellow Premier League club Aston Villa once he had returned from international duty with Argentina.

[30] On 9 August 2023, on the eve of the Premier League season, Buendía suffered what was described as a "significant knee injury" in training and would require a scan and treatment from a specialist.