The Argentine World Player of the Year netted twice in a 4-1 victory at Real Zaragoza to notch up 38 La Liga goals in the campaign and his 60th in all competitions.
Gerd Muller was the last player to achieve the feat on the way to scoring 67 goals for Bayern Munich in the 1972/73 season and Messi has at least 10 more matches in which to break the German's record.
Messi put Barca 2-1 ahead with a powerful strike into the roof of the net shortly before half-time and also netted from the penalty spot in the closing stages at the Romareda.
Still only 24, he is already Barca's leading scorer in official games with 240 goals, beating Cesar Rodriguez's 60-year-old record of 232 last month when he also became the first player to score five in a Champions League match.
Messi netted his first goal for the Catalan club on May 1, 2005 aged 17 years, 10 months and seven days in a La Liga game against Albacete at the Nou Camp after coming through the youth system with contemporaries Cesc Fabregas and Gerard Pique.
This season, as well as his La Liga tally, Messi has 14 goals in the Champions League, two in the King's Cup, three in the Spanish Super Cup, one in the European Super Cup and has also scored two at the Club World Cup.
He has 11 more goals than Real Madrid forward Cristiano Ronaldo, who has 37 in La Liga, eight in the Champions League, three in the King's Cup and one in the Spanish Super Cup.
Other players who have scored 60 or more goals in a season include Fernc Deak, who netted 66 for Hungarian club Szentlorinc in 1945/46, Henk Groot, who struck 64 times for Ajax Amsterdam in 1960/61 and Dixie Dean, who got 63 for Everton in 1927/28.
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