Born in Elche, Alicante, Valencian Community, Giménez was a product of hometown club Elche CF's youth system. He made his debut for the first team on 22 September 2007 in a 1–2 away loss against Real Sociedad, and played six more Segunda División matches with the main squad in that season. In January 2010, Álvaro signed with neighbouring Valencia CF who had already tried to acquire the player the previous year. He was assigned to the B-team, appearing rarely as they suffered relegation from the third level. Álvaro returned to his hometown for the 2010–11 campaign, performing consistently at amateurs Torrellano Illice CF in division four. On 4 July 2011, he joined RCD Mallorca B in the third tier, being promoted to the main squad shortly after and making his La Liga debut on 29 October in a 0–5 loss at FC Barcelona. Álvaro's first two goals in the top flight earned the Balearic Islands side four points, as he scored against Athletic Bilbao and Sporting de Gijón – on both occasions, he was fielded by manager Joaquín Caparrós in the starting XI. However, in August 2012, he underwent surgery to correct a pubalgia ailment, being sidelined until November. Álvaro moved to Elche CF in summer 2013, being initially assigned to the reserves in the third division. In October, he suffered a serious knee injury which sidelined him until May of the following year. On 19 August 2014, Álvaro signed a new two-year deal with the Franjiverdes and was promoted to the first team. On 29 June 2016, he moved to AD Alcorcón of the second tier after agreeing to a two-year contract. On 2 July 2018, free agent Álvaro joined another Segunda División club, UD Almería, on a two-year contract. He finished the campaign as the division's top goalscorer with 20 goals; highlights included a hat-trick in a 5–3 home defeat of his former club Elche on 12 May 2019. Having activated Álvaro's €1.5 million release clause, English Championship club Birmingham City signed him on 6 August 2019 on a three-year contract. He had a difficult debut, coming into the visit to Nottingham Forest after an hour with his side two goals down and struggling. He started the next match, at home to Barnsleythree days later, and won the ball that led to Lukas Jutkiewicz's opening goal before controlling a lofted pass from Steve Seddon on his chest and lobbing the goalkeeper to complete a 2–0 win. With no goals to show for all his hard work, by mid-November Álvaro had lost his place to Kerim Mrabti. With Jutkiewicz rested for the 27 November visit to Sheffield Wednesday, Álvaro opened the scoring in a 1–1 draw with a goal that head coachPep Clotet hoped would restore "calm and confidence" to the player. He scored again ten days later in a win away at Reading, but soon lost form and made his last appearance for the club on 1 January 2020. On the final day of the January 2020 transfer window, Álvaro signed for 2019–20 Segunda División leaders Cádiz CF on loan until 30 June, with the intention of making the move permanent. He made four first-team appearances without scoring in the month before football in Spain was suspended because of the COVID-19 pandemic. He scored in his first match after the resumption, a late equaliser at home to Rayo Vallecano, and his loan spell was extended to cover the remainder of the season. Having achieved promotion to the top flight, Cádiz duly took up their option and Álvaro signed a two-year contract.
