Maxi Rodriguez was born and brought up in Rosario by his grandparents and mother as his father had abandoned the family. It was a struggle but Maxi was a strong character and first came to prominence with local club Newell's Old Boys. He played for the club for three seasons, scoring 20 times in 59 league matches, before moving on loan half a season to second division Real Oviedo in Spain. He starred for Argentina in the 2001 World Youth Championship, scoring four goals, including one in the 3-0 win over Ghana in the final. A year later he moved permanently from Argentina to La Liga's Espanyol in time for the 2002/03 season. Maxi's reputation grew in Barcelona and he earned himself a transfer to Atletico Madrid in 2005. After a good opening season, injury restricted him to just ten league matches in his second campaign. By this time he had already come to the attention of his international manager and was included in Argentina's squad for the 2006 World Cup in Germany, where he showed the world what he could do with a sensational extra-time winner as Argentina defeated Mexico. Atletico Madrid and Liverpool were placed in the same Champions' League group in the 2008/09 season. Rodriguez scored Atletico's goal in their 1-1 draw at Anfield but Rafa Benítez was already aware of the player's capabilities. Liverpool made their move in January 2010 and Maxi was introduced to his new home public before Liverpool's FA Cup replay with Reading in the middle of the month.
Maxi admitted to a little he had told Rafa when he signed for Liverpool as he told the Liverpool Echo in 2020: "“He asked me if I knew how to speak the language and I said 'yes, of course, stay calm.' Of course, I didn't want the negotiations to fail so I told a little lie. When I arrived in England, there was a press conference and Rafa told me he would speak first and then I would continue. That was when I grabbed him and said 'look Rafa, I need to confess something to you. I don't know English. The only thing I know is how to say hello. Rafa said 'you're a son of a b****.'"
The 29-year-old who could operate both in midfield and on the wing proved to be a good squad player. The manager showed great faith in the Argentinian by starting him in 13 fixtures between 6 February and 2 May 2010. In the World Cup in South Africa Maxi made four starts and one substitute appearance as the double World champions reached the quarter-finals. Rafa was soon his way out of Anfield and Maxi was used sparingly by Roy Hodgson. Thankfully the Englishan's reign was short and the Argentinian was more of a regular under Kenny Dalglish. Maxi came to prominence towards the end of the 2010/11 season with a flurry of goals, scoring seven times in three successive Premier League matches including hat-tricks against Birmingham City and Fulham. He made twice as many first-team appearances as he did in 2009/10. Ten goals in 35 matches showed Maxi's ability to arrive in the nick of time from midfield to finish off a well-worked attack. Even though Maxi only appeared in just over 40% of Liverpool's first-team matches in 2011/12, he again proved that he had an eye for a goal, scoring twice in away matches at Chelsea in the League and the League Cup in November and then scoring twice at Blackburn towards the end of the season, a total of six goals in 17 starts.
On 13 July 2012 Maxi returned to his first club, Newell's Old Boys, in his hometown, Rosario. On the same day Maxi addressed Liverpool's supporters in an open letter: "Dear Reds, I am leaving Liverpool FC today. Before signing for LFC, I just saw the club as one of the greatest institutions in football. After my time here I can confirm that this is not just a great club but also a great family. I have tried to give everything every day that I was wearing the LFC crest. It has been a great honour to defend this shirt during two and a half years. I am returning home with a suitcase full of great memories, good friends within the team and also within this great family that works every day in the club. Thanks a lot for your support. You can NOT imagine what a great honour it was for me when the Kop sang, 'Maxi, Maxi Rodríguez runs down the wing for me da da da da dada...' Hasta la vista!"
Maxi played in twelve first-team matches for Newell's during the second half of the calendar year of 2012; and he also continued to be selected regularly when the Torneo Final and Copa Libertadores matches resumed in February 2013. In the Torneo Inicial (3 August 2012 - 13 February 2013) Newell's finished second behind Vélez Sarsfield. But Newell's won the Torneo Final (a competition that ran from 8 February until 23 June 2013) and Maxi won the Best Player in the League award. He comfortably made Alejandro Sabella's provisional 26-man squad for the 2014 World Cup finals in Brazil and in the tournament scored the deciding penalty in the shoot out against Holland in the semi final. Maxi remained at Newell's for three more years before moving to Penarol in Uruguay. On 1st January 2019 he returned to Newell's for a third spell, being appointed as captain and scoring three times in the seven starts he made over the remainder of the season. In 2019/20 he started all 23 league games prior to the suspension of the season due to Covid 19 and remained at the club for the start of 2020/21, appearing in the first two League Cup games of the new season.