The 26-year-old - who scored 46 goals in 32 La Liga appearances last season and has eight in 11 league games so far in 2013-14 - tore the leg muscle in a 4-1 victory over Real Betis on November 10.
Medical tests confirmed Messi will spend around six to eight weeks on the sidelines during his rehabilitation, with the final part of his recuperation seeing him head home to his native Argentina on Friday.
Club doctor Ricard Pruna and physiotherapist Elvio Paulorroso will jet out to Buenos Aires in mid-December to check on Messi's progress as he bids to return to action after the mid-season break following an injury-hit start to the season.
"The latest tests on the player have shown that the recovery programme is going to plan," read a statement on Barca official website.
In Messi's absence, Barca beat Granada 4-0 last weekend before slipping to a 2-1 defeat at Ajax in the UEFA Champions League in midweek.
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