[12] Curran made his senior debut in a Twenty20 match in the NatWest t20 Blast tournament against Kent at The Oval on 19 June 2015, aged 17 years and 16 days.

[15] He made his List A debut in a Royal London One-Day Cup match against Northamptonshire at The Oval on Thursday 27 July 2015.

[17][18] In March 2019, he was named as one of eight players to watch by the International Cricket Council (ICC) ahead of the 2019 Indian Premier League tournament.

[27] Later the same month, in the County Championship match against Kent, Curran scored his maiden century in first-class cricket, with 126 runs.

[29] He represented England Under-19s at the 2016 ICC Under-19 Cricket World Cup,[30] where he played all six games, scoring 201 runs and taking seven wickets to help his team finish sixth.

He was selected for the England Lions for their 2016–17 tour of the United Arab Emirates, and again for their match against South Africa A at Canterbury in the 2017 season.

Curran received his first senior call-up for England in January 2018 for the 2017-18 Trans-Tasman Tri-Series against Australia and New Zealand,[31] but did not play any games.

[40] Curran played two Tests during England's tour of Sri Lanka in November 2018, scoring 112 runs at an average of 37.33, but only took a single wicket.

[44] Curran played two Tests in the 2019 England tour of the West Indies, making 50 runs in four innings and taking one wicket at an average of 161.

In South Africa, Curran made 130 runs in 7 innings, and took 10 wickets at an average of 32.6, which included career best figures of 4/58 in the first Test.

[45][46] On 29 May 2020, Curran was named in a 55-man group of players to begin training ahead of international fixtures starting in England following the COVID-19 pandemic.

[47][48] On 17 June 2020, Curran was included in England's 30-man squad to start training behind closed doors for the Test series against the West Indies.

[51][52] In the 2020 England summer, Curran played in one Test against the West Indies and one against Pakistan, scoring 17 in his only innings and taking 4 wickets at an average of 36.

[58] However, on 5 October 2021, Curran was ruled out of England's squad due to a back injury,[59] with his brother, Tom, named as his replacement.