Messi limped off the field during his side's 2-0 win over Almeria at the end of last month having opened the scoring in the 21st minute to take his season tally to 11 goals in just seven games.
The four-time World Player of the Year has already missed two games for Barcelona with the injury, including the 1-0 win over Celtic in the Champions League a fortnight ago.
Messi was also ruled out of Argentina's World Cup qualifiers against Peru and Uruguay, although his side have already booked their spot in next year's tournament.
The 26-year-old stayed at his club during the international break and was one of 11 first-team players to take part in a training session with manager Gerardo Martino on Monday.
Barcelona, who have won all eight of their league games so far this season, face Osasuna on Saturday before a Champions League encounter with AC Milan three days later.