Sodje sustained the problem during last weekend's home friendly against Blackburn, where he scored in a 2-2 draw, and will not face Barnsley at Hillsborough on Saturday.
Boss Brian Laws told The Star: "Obviously it's a blow to lose Akpo for Saturday and I feel desperately disappointed for the lad because he has worked so hard in pre-season.
"But let's be positive, he will be back in a matter of weeks and in the meantime I am confident we have the strikers to score the goals that will hopefully see us get off to a great start to the new season."
Laws was able to report more positive news on the injury front regarding Sodje's fellow forward Leon Clarke, who is in with a chance of facing the Tykes despite a hamstring niggle.
"We'll assess Leon as the week goes on and I'm certainly not ruling him out for Saturday," Laws added. "He's done it before and played in the next game after having a bit of a hamstring niggle."