After impressing in a trial and being approved for a work permit, Martinez was formally registered as an Arsenal player in July 2010. After injuries to Ryan Clarke and Wayne Brown, and the termination of Connor Ripley’s loan, Martínez went on emergency loan to Oxford United, making his debut in the Football League in their final game of the season against Port Vale in League Two on 5 May 2012; Port Vale won 3–0. Later that year, Martinez was named on the Arsenal substitute bench for their fixtures away at Stoke City on 26 August and against Liverpool on 2 September, as cover for the injured Wojciech Szczęsny and Łukasz Fabiański, respectively. On 26 September, he made his Arsenal debut in a 6–1 home win against Coventry City in the third-round of the League Cup. He made his second Arsenal appearance in the following round in a 7–5 win away to Reading. Martínez subsequently transferred to Championship club Sheffield Wednesday on an emergency 28-day loan on 15 October 2013. He made his debut for Wednesday on 23 November, against Yorkshire rivals Huddersfield Town. Martínez’s loan was eventually extended until the end of the season. After returning to Arsenal, Martínez was an unused substitute as Arsenal won the 2014 FA Community Shield on 10 August, with a 3–0 win over Manchester City at Wembley Stadium. He made his debut in the Champions League soon after, helping Arsenal defeat Anderlecht 2–1 in the group stage. He then made his Premier League debut as a 2nd half substitute, replacing the injured Szczęsny against Manchester United at the Emirates Stadium on 22 November. With injuries to backup goalkeeper David Ospina, Martínez played his second Champions League game on 26 November, keeping a clean sheet in a 2–0 victory over Borussia Dortmund. His “faultless” performance in the match led to him being named in the UEFA Team of the Week. He made his first Premier League start on 29 November against West Bromwich Albion, and also started against Southampton four days later; he kept two clean sheets as Arsenal won both matches 1–0. On 20 March 2015, Martínez joined Championship club Rotherham United on an emergency loan until the end of the season. He made his debut the following day against South Yorkshire rivals Sheffield Wednesday, conceding two added-time goals in a 3–2 home defeat. On 2 August, Martínez was an unused substitute as new signing Petr Čech played for Arsenal in the 2015 Community Shield, a 1–0 win over rivals Chelsea. On 11 August, he joined Championship club Wolverhampton Wanderers on a season-long loan. After making 15 appearances in the opening months of the campaign, he suffered a thigh injury that kept him out of contention for several months and was unable to regain his starting place afterwards. He spent the 2016–17 season at Arsenal, and played five matches during the campaign, including two Premier League appearances against Crystal Palace and West Ham United. On 2 August 2017, he joined La Liga club Getafe on a season-long loan, and on 23 January 2019, he was loaned to Championship club Reading until the end of the season. At Reading, Martínez made his debut on 29 January against Bolton Wanderers, and won the man of the match award against Aston Villa a few days later.