Born in Buenos Aires, Otamendi made his Primera División debut for Club Atlético Vélez Sarsfield on 10 May 2008, in a 2–1 home win against Rosario Central for the Clausura tournament. During manager Hugo Tocalli’s spell he was only fifth-choice stopper, behind Waldo Ponce, Fernando Tobio, Marco Torsiglieri and Mariano Uglessich. However, his role in the first team changed during Ricardo Gareca’s first season as head coach, the 2009 Clausura: he replaced Ponce for the third game after the Chilean was injured while playing for his national team, and eventually won a starting position alongside Sebastián Domínguez, playing 17 of the 19 games in Vélez’s winning campaign.

In April 2009, Otamendi was called up by Argentine national team coach Diego Maradona for a friendly with Panama. At the time of his selection he had only played 11 professional games, and eventually started the match on 20 May, in a 3–1 win.

On 23 August 2010, Otamendi was transferred to Portuguese side FC Porto on a €4 million fee, signing a five-year contract. Vélez also retained 50% of his registration rights, with the player having a pre-set price of another €4 million to be met by Porto prior to September 2011. He netted in his first match, a 2–0 home victory over S.C. Olhanense, finishing his first season with 15 appearances and five goals (notably both in a 2–0 away win against S.C. Braga) as the northerners won the Primeira Liga championship.

During the 2010 FIFA World Cup qualifying campaign, Otamendi played as a centre back alongside Martín Demichelis against Ecuador (0–2 away loss), partnered former Vélez teammate Domínguez against Brazil in a 1–3 home defeat and appeared as a right back in a 1–0 win in Uruguay which sealed the country’s qualification to South Africa. On 19 May 2010 he was confirmed as part of the 23-men squad for the final stages, featuring in the starting eleven for the final group stage game against Greece; on the press conference after the match, Maradona said that, in his opinion, he was the best player on the field.

On 6 September 2011, Porto exercised the rights to sign the remainder of Otamendi’s playing rights. He played 30 official games during the season to help the club to another two major titles, notably the back-to-back domestic league.

Otamendi scored his first goal for Argentina on 2 September 2011, in a 1–0 friendly win over Venezuela in Kolkata, after heading a corner taken by Lionel Messi. After being cut from the squad that later appeared at the 2014 World Cup, he was selected by coach Gerardo Martino for the 2015 Copa América, playing the entirety of all but one match as they lost to hosts Chile on a penalty shootout in the final; he was named in the Team of the Tournament.

On 5 February 2014, Otamendi was sold to Valencia CF in La Liga for €12 million, on a five-year contract starting on 1 July. He was immediately loaned to Clube Atlético Mineiro in Brazil, and played 19 times for the team from Belo Horizonte, scoring once to open a 4–1 win at city rivals América Futebol Clube (MG) on 23 March in the first leg of the semi-finals of the state championship.

Otamendi made his debut in the Spanish top level on 23 August 2014, starting in a 1–1 away draw against Sevilla FC. He scored his first goal for his new club on 4 October, helping to a 3–1 home success over Atlético Madrid.

On 4 January 2015, Otamendi headed Valencia’s winner in a 2–1 home win over Real Madrid, ending their opponents’ club record 22-match winning streak as a result. After helping Los Che qualify for the UEFA Champions League for the first time in four years, becoming the first club stopper to score six goals in the league in the process, he was the only player from his team to be named in the La Liga Team of the Year.

On 31 October 2015, Otamendi scored his first goal for the club in a 2–1 home win over Norwich City. He played the full 120 minutes as they won the Football League Cup on 28 February 2016, defeating Liverpool on a penalty shootout in the final.

Otamendi started all the games in the Copa América Centenario in the United States, in which Argentina again both faced Chile in the tournament final and lost in a penalty shootout, 2–4. In the second group match against Panama, on 10 June 2016, he scored the opening goal in a 5–0 win.

On 10 December 2017, Otamendi scored the winning goal in the Manchester derby at Old Trafford, helping City stretch their lead at the top of the Premier League to 11 points. City would go on to lift the Premier League title that season with a record-breaking 100 points, this was Otamendi’s first league title in England. On 18 April 2018, Otamendi was named in the PFA Team of the Year alongside Manchester City teammates Kyle Walker, David Silva, Kevin De Bruyne and Sergio Agüero.

On 29 September 2020, Otamendi joined Benfica on a three-year contract, for a €15 million fee.