Elokobi suffered a fractured and dislocated ankle in the first half of City's 3-2 defeat to Leeds United on Saturday.
McInnes told the club's official website: "All our thoughts are with George because it's a horrendous injury and he won't play again this season.
"He's fractured and dislocated his ankle and has gone off immediately for an operation.
"We wish him well and it's a real shame because he was so happy with this move and we were excited to be working with him."
An English-based player for most of his career, Elokobi joined Wolves in January 2008 from Colchester United, and has previously spent time on loan at Nottingham Forest.