The four-time Ballon d'Or winner suffered the blow in Sunday's 4-1 win over Real Betis, and took to his Facebook page to explain the extent of his work.
"As many of you know, over the next few weeks I will be working full time on the recovery of this new injury, for me it is a pity not to play with my team right now," Messi wrote.
"Now what is most important is to recover well to help my teammates and give back all the support you have given to me in the best way I know how to do, playing football.
"Thank you for your messages!"
Messi has scored 14 goals in 14 games for Barca this season.