The Argentine World Player of the Year netted twice from the penalty spot and once from open play to help Barca to a 4-1 win at home to Malaga, his 44th, 45th and 46th La Liga goals of the campaign taking his total in all competitions to 68.
Muller set the record playing for Bayern Munich in the 1972/73 season and Messi has three more matches - two in La Liga and the King's Cup final - in which to add to his tally.
Messi's third of the night at a festive Nou Camp showcased his dazzling skills as he raced clear on to Andres Iniesta's pass, dinked the ball over the onrushing Carlos Kameni and tapped the ball into the empty net.
Clutching the match ball and with a typically shy expression on his face, he was congratulated by his team-mates as he strolled off the pitch at the end.
Still only 24, Messi is already Barca's leading scorer in official games with 248 goals, beating Cesar Rodriguez's 60-year-old record of 232 in March when he also became the first player to score five in a Champions League match.
He 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, he has scored 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 two at the Club World Cup.
He has 11 more than Real Madrid forward Cristiano Ronaldo, who has 43 in La Liga, 10 in the Champions League, three in the King's Cup and one in the Spanish Super Cup.
