He has participated for the U-21, the U-23, and the senior levels of Mexico's national team. He has represented Mexico at the 2016 Summer Olympics and the 2017, 2019, and 2021 CONCACAF Gold Cups.
In December 2016, Pachuca announced Pizarro was transferred to Guadalajara for a reported $15 million, in a deal that saw Víctor Guzmán go the other way, permanently joining Pachuca.[7][8] On 7 January 2017, Pizarro made his debut against Club Universidad Nacional, playing the whole match in which Guadalajara won 2–1.[9] A week later, Pizarro scored his first goal for Guadalajara against Monterrey from a long range shot, the game ended 2–2.[10]
In April, Guadalajara won the Clausura Copa MXfinal against Morelia.[11][12] The following month, Pizarro would prove to be vital during the Clausura championship, managing to score in the first leg of the final against Tigres UANL as Guadalajara would go on to win the title, finishing an eleven-year-long drought of league titles.[13][14][15] As a result, Guadalajara won their first Double since the 1969–70 season.[16]
On 4 June 2018, after much media speculation, Guadalajara sporting director Francisco Gabriel de Anda officially announced that Pizarro was being transferred to fellow league club Monterrey,[23] for a reported $16 million, making him the costliest interleague transfer in Liga MX history.[24] Rejoining former Pachuca manager Diego Alonso, Pizarro would make his debut with Monterrey on 21 July 2018 in a 1–0 victory against his youth club, Pachuca.[25] On 5 November, he would score his first goal with the team in a 2–0 win over Veracruz.[26]
He was an integral part of the team as he helped Monterrey win the 2019 CONCACAF Champions League Finals title against crosstown rivals Tigres UANL, their fourth title.[27] This made Pizarro alongside teammate Angel Zaldívar the first players to win the tournament in back–to–back years with two different teams.[28] Following the end of his first season with Monterrey, he was listed in the Best XI of the Clausura.[29]
Following an impressive campaign with Mexico over the summer, Sky Sport Italia linked Pizarro with A.C. Milan.[30] On 14 December, following Monterrey's 3–2 quarter-final victory over Al Sadd at the 2019 FIFA Club World Cup, he was named Man of the Match.[31] At the end of the month, he would win the Apertura championship against América, with Pizzaro being handed a starting berth in both legs of the final.[32]
Inter Miami
On 14 February 2020, Pizarro left Monterrey for Major League Soccer expansion side Inter Miami, following a protracted dispute between the clubs about the activation of his release clause, rejoining head coach Diego Alonso for a third time, his coach at both Pachuca and Monterrey.[33] The following day, despite not officially being announced as a signing for the club, Pizarro scored the first goal for Miami in a 2–1 preseason friendly loss to Philadelphia Union.[34] That same day, Monterrey filed a complaint with FIFA against Pizarro and Inter Miami for improper contact between the player and Inter Miami co-owner David Beckham while Pizarro was still under contract with Monterrey. FIFA's investigation was still on-going when news of the complaint broke on 4 March.[35]
Pizarro was loaned out to his previous club Monterrey for 2022, with an option to make it permanent.[40]
On 14 July 2023, Inter Miami and Pizarro agreed to mutually terminate their contract.[41]
AEK Athens
On 17 July 2023, Pizarro signed a two-year contract with Super League Greece club AEK Athens with an option to extend his contract for another year.[42] The move had him rejoin former Guadalajara manager Matías Almeyda and former Guadalajara teammate Orbelín Pineda.[43] Pizarro assisted a goal in a 2-1 away against Dinamo Zagreb (Ch. League qualifier).
On 7 July 2016, Pizarro was named in Mexico's 18-man squad that would participate in the 2016 Summer Olympics in Rio de Janeiro, Brazil.[49] In Mexico's first group stage match against Germany, he scored Mexico's second goal to make the game 2–1 but was eventually tied 2–2.[50] In Mexico's second group stage match against Fiji, Pizarro along with teammate Oribe Peralta, would pick up injuries.[51] They were subsequently replaced by Carlos Fierro and Raúl López Gómez.[52]
Senior
On 29 January 2014, Pizarro made his senior national team debut in a friendly game against South Korea, playing all 90 minutes.[53] On 10 February 2016, Pizarro scored his first goal for Mexico in the 87th minute of the friendly match against Senegal, with the match finishing 2–0.[54][55]
With the arrival of Gerardo Martino as Mexico's new coach, Pizarro has been given precedence.[61][62] In March 2019, Pizarro declared that it was a motivating gesture that Martino treated the domestic league players with the same importance and opportunity as those based in Europe.[63] He was included in Mexico's preliminary list for the 2019 CONCACAF Gold Cup[64] and was eventually in the final list.[65] Prior to the start of the Gold Cup, he picked up a minor injury and did not appear in the tournament until the final group stage match against Martinique,[66][67] coming on as a half-time substitute and contributing an assist to Raúl Jiménez for Mexico's second goal in a 3–2 victory.[68][69] In the final against the United States, during the first half he would bend his left elbow in an apparent injury but managed to play in the second half as well, managing to contribute in Mexico's build up play for the winning goal as they won the tournament.[70]
He has been described as "A classy operator of the ball, Pizarro can pick a pass, unlock tightest of defenses and has the guile to operate as a number 10. The Mexican star can spark creativity from midfield and add [fluency in the] build-up play in the final third. He is tenacious and hard-working, whilst also possessing the ball retention skills and the intelligence to get into promising goalscoring positions. Not only that, but the Tampico-born star also has a hammer of a right foot that is capable of delivering rockets from long distances. He has the ability to hold the ball in tightest of situations and his wonderful technique allows him to run comfortably with it."[79] Various outlets have described him as a difference maker in critical moments.[70][78] He also plays as an inverted winger, having the tendency to move to the inside of the pitch as the full-backs move upward so he can thrive.[62][80]