The 28-year-old forward has scored seven goals for the Owls since his summer arrival from Port Vale, but will now sit out the rest of the campaign as he requires surgery.
Boss Brian Laws said: "Akpo is going in for an operation on his ankle and it's a big, big blow for myself and the team, but first we must concentrate on getting his ankle better for the long term.
"He has been an inspiration for us this season, some of his performances have been outstanding and his enthusiasm second to none. He will be a big miss."
Laws is now set to move into the loan market to try and find a replacement for the stricken Sodje.