The Catalans beat Deportivo 2-0 at the Camp Nou on Saturday and Messi came off the bench to register his 40th league goal of the season in the 88th minute. The 25-year old netted his 27th goal in 17 matches.
According to the Catalan giants, Messi broke Polish forard Teodor Pewterek's 1937-38 record of scoring in 16 successive games for Ruch Chorzow.
Barcelona confirmed on their official website saying: "The Argentine player's tally represents a new record in the history of football, something no other player has achieved before."
However, FIFA is yet to confirm Barcelona's claim.
The World Player of the Year has now scored 52 goals in all competitions this season. Messi broke another world record of hisghest number of goal scored in a calendar year, beating gerd Mueller's 1972 tally of 85.
Meanwhile, Barcelona are preparing to overturn a two-goal deficit against AC Milan in the second leg of their Champions League last 16 tie. Coach Jordi Roura rested some of the stars, including Messi, for the game against Deportivo.
Prior to this game, Barcelona suffered three defeats in four games. The loss to Milan at the San Siro followed by Copa Del Rey exit at the hands of Real Madrid and then the league loss at the Bernabeu five days later.
The 2-0 victory took Barcelona 14 points ahead of second-placed Atletico Madrid.