The 28-year-old defender has gone under the knife and will miss the start of the season.
"Kelvin is going to be out for around three months which is a big blow to us," boss Aidy Boothroyd said on the club website.
"With Kelvin out for that length of time it's an opportunity for others.
"I've got to give that a bit of thought and my main focus is making sure that when we go into the game at York (on the opening day of the season) we have the strongest team possible.
"Roy O'Donovan is fine and Clive Platt and Chris Hackett will probably be available for selection for the second week of the season."