Born in Moncada, Valencian Community, Iborra was a product of Levante UD’s youth system. He made his first-team debuts during the 2007–08 season, as the club’s severe financial problems prompted the exit of several players. After appearing in a Copa del Rey match against Getafe CF on 9 January 2008, he played in La Liga against Real Madrid four days later (0–2 home loss).

On 30 March 2008, Iborra scored his first Levante goal, a last-minute effort in a 1–2 loss at UD Almería. In the 2009–10 campaign, as the side returned to the top flight after a two-year absence, he was one of the team’s most used players — 36 games, 2,640 minutes — netting once.

Iborra joined fellow league club Sevilla FC on 16 August 2013, after agreeing to a five-year contract. He finished his debut season with 41 games and four goals all competitions comprised, including 12/1 in the UEFA Europa League which his team won.

In 2014–15, Iborra was often deployed in a more attacking midfield role by manager Unai Emery, and responded by scoring nine goals overall. On 24 September 2016 he filled in as the goalkeeper for the final two minutes away to Athletic Bilbao when Salvatore Sirigu was sent off, conceding a penalty from Aritz Aduriz in a 1–3 loss.

Sunderland agreed to pay Sevilla £7 million for Iborra, but called it off on 30 August 2016 as the summer transfer window came to a close. Under new coach Jorge Sampaoli he started the new season as a reserve but, on 11 December, after having replaced the injured Nicolás Pareja at half-time of the away fixture against RC Celta de Vigo, he netted a hat-trick which included a late penalty in a 3–0 win.

On 6 July 2017, Leicester City announced they had signed Iborra on a four-year contract for £15 million. After picking up a groin injury during pre-season, he did not make his debut until 19 September, when he played the whole of a 2–0 home win over Liverpool in the EFL Cup and provided the assist for Shinji Okazaki’s goal. His maiden Premier League appearance took place on 30 September as he played the second half of a 0–0 draw away to AFC Bournemouth, and he scored his first goal in the latter competition on 4 November in a 2–2 draw at Stoke City.

On 7 January 2019, Iborra joined Villarreal CF on a four-and-a-half-year deal for a reported fee of £9 million. He cited the failure of his family to adjust to life in England as the main reason for his departure.