Elneny played his youth football with Al Ahly. In 2008, he transferred to Al Mokawloon during the 2010–2011 season. Elneny advanced and became a regular in the starting team. Following the Port Said Stadium disaster in early February 2012, the Egyptian Premier League was stopped and all subsequent matches of the 2011–12 Egyptian Premier League were postponed. On 10 March 2012, the Egyptian Football Association announced their decision to cancel the remainder of the season.

FC Basel had been watching Elneny for some time and invited him to their training camp in Estepona from 14 to 24 January 2013. Elneny played his unofficial debut on 18 January 2013 during the friendly match against Steaua București, a 1–1 draw. Elneny was able to impress Basel’s trainer Murat Yakin during the training camp and on 29 January 2013, it was announced that he had signed a loan contract with Basel up until the end of June 2013. Elneny played his official debut for Basel in the 2012–13 Swiss Super League season on 10 February 2013 in the 3–0 home win against Sion as he was substituted in at half time.

During May 2013 Basel announced that they had taken up the option of signing the Egyptian midfielder on a permanent basis. He signed a four-year contract up-until 30 June 2017. He scored his first goal for Basel, the last goal of the match, in the 4–2 home win at the St. Jakob-Park against Zurich on 16 April 2014. At the end of the 2013–14 Super League season Elneny won the league championship with Basel. They also reached the final of the 2013–14 Swiss Cup, but were beaten 2–0 by Zürich after extra time. During the 2013–14 Champions League season Basel reached the group stage and finished the group in third position. Thus they qualified for Europa League knockout phase and here they advanced as far as the quarter-finals. In their season 2013–14 Basel played a total of 68 matches (36 Swiss League fixtures, 6 Swiss Cup, 6 Champions League and 10 Europa League and 10 test matches). Elneny totaled 55 appearances, 32 League, 4 Cup, 6 Champions League and 6 Europa League as well 7 in the test games. He scored just that one goal in the league.

The season 2014–15 was a very successful one for Elneny and FC Basel. The championship was won for the sixth time in a row that season and in the 2014–15 Swiss Cup they reached the final. But for the third season in a row, they finished as runners-up, losing 0–3 to FC Sion in the final. Basel entered the Champions League in the group stage and reached the knockout phase as on 9 December 2014 they managed a 1–1 draw at Anfield against Liverpool. But then Basel then lost to Porto in the Round of 16. Basel played a total of 65 matches (36 Swiss League fixtures, 6 Swiss Cup, 8 Champions League and 15 test matches). Under manager Paulo Sousa Elneny totaled 51 appearances, 29 in the Super League, 6 in the Cup and 7 in the Champions League, as well 9 in test games. He scored 5 goals in these matches.

On 13 January 2016, after a 3–3 draw against Liverpool, Arsenal manager Arsène Wenger confirmed the signing of Elneny from FC Basel. The following day, the transfer was officially confirmed by the club for an undisclosed fee reported to be somewhere between £5 million and £7.4 million. He was assigned the number 35 shirt for Arsenal. He made his debut for the club in a 2–1 win against Burnley in the fourth round of the FA Cup, on 30 January. Elneny scored his first Arsenal goal in the Champions League Round of 16 second leg defeat against FC Barcelona, and was later awarded Arsenal’s Player of the Month award for March. He also starred in April combining well with Aaron Ramsey, winning the Arsenal’s Player of the Month award for a second month. Elneny’s only goal won him the goal of the season award for Arsenal. In the 2017/18 season, on 7 December 2017, Elneny scored his first goal at the Emirates Stadium (his second for Arsenal overall) in the Europa League Group Stage against FC BATE Borisov in a match which ended 6–0 to the home side. On 15 February, Elneny again produced a commendable display in the first leg of Arsenal’s round of 32 Europa league tie against Östersunds FK. Elneny was subsequently rewarded man of the match for his effort in a 3–0 away victory.

On 26 March 2018, Elneny renewed his contract with Arsenal.

On 8 April 2018, Elneny was sent off against Southampton. In a tight game defender Jack Stephens tussled with Jack Wilshere and retaliation from Stephens resulted in referee Andre Marriner giving him a straight red. Wilshere escaped with just a yellow card but in the aftermath, Elneny received a red card after a shove on Cédric Soares. Arsenal held on to win 3–2. On 1st November 2020, Elneny put in an excellent display at the base of Arsenal’s midfield alongside Thomas Partey to render Bruno Fernandes and Paul Pogba ineffective and earn Arsenal a first league win at Old Trafford since 2006. Elneny was praised by manager, Mikel Arteta after the game.

On 31 August 2019, Elneny joined Beşiktaş J.K. on a season-long loan deal with an optional buyout clause.

In July 2019 the body of a man, believed to be a thief attempting to steal electrical cables, was discovered on Elneny’s property in El-Mahalla El-Kubra, Egypt. The body was discovered by his father, who immediately reported the incident to the police. It is believed that the man was electrocuted trying to steal the cables.