Born in Santa Elena, Entre Ríos, Caballero started his playing career with Boca Juniors in 2001, where he won three major titles in 2003.

[4] Caballero joined Elche of Spain in 2004, and when his daughter was diagnosed with cancer he agreed to a brief loan spell back in his country with Arsenal de Sarandí to care for her, published on Ivoox.

On 1 October 2011, Caballero entered Málaga's history books as he kept his goal clean for 480 minutes, beating the club's previous record of 429 held by Pedro Contreras since the 2001–02 season.

[13] On 8 July 2014, Caballero signed a three-year deal with Manchester City, for a fee believed to be in the region of £6 million excluding add-ons.

He reunited at his new club with former Málaga manager Manuel Pellegrini,[14] and his competitive debut came on 10 August in the 2014 FA Community Shield, playing the full 90 minutes in a 0–3 loss to Arsenal at Wembley Stadium;[15] a week later, in the Premier League opener, he was an unused substitute at Newcastle United.

[17] He made his first league appearance away against Hull City three days later, relegating longtime incumbent Joe Hart to the bench in a 4–2 win.

[19][20] Throughout the season, he was first-choice in the League Cup, receiving criticism in the national press before the final following a poor performance in the 1–5 loss to Chelsea in the FA Cup;[21] in the decisive match at Wembley Stadium, he saved three attempts in the 3–1 penalty shootout triumph against Liverpool,[22] and Pellegrini subsequently said he would rather lose the match to keep his word, whilst several pundits added that both player and manager deserved an apology with some remarking the performance was a lesson in loyalty.

[33] On 17 January 2018, Caballero saved a penalty from Nélson Oliveira in the shootout of a third round FA Cup replay win over Norwich City, which had finished 1–1 after extra time.

[34] Due to an ankle injury to first-choice Thibaut Courtois, he made his Premier League debut away to Brighton & Hove Albion two days later, in a 4–0 success.

[36][37] With Arrizabalaga struggling to stay in form during the 2019–20 Premier League season, Caballero was selected as the starting goalkeeper for Chelsea in a cup match against Hull City in late January 2020.

[42] On 4 June 2021, Chelsea announced he would depart from the club at the end of the month when his contract expired, and thanked him for his contribution to the team with an extended article for his time and feats there.

[54] He started the tournament due to the injury of habitual first-choice Sergio Romero,[55] and made his debut in the competition on 16 June in a 1–1 group stage draw against Iceland.