The 28-year-old defender damaged a ligament during training and the League Two club are awaiting the results of scans.
Brewers boss Gary Rowett told the Burton Mail:"It's nothing too sinister but it's enough to keep him out for the first month or so.
"We're hoping if the scan is positive he'll be back playing in a couple of weeks.
"It's a shame for Zander because he started pre-season well but I was potentially looking to bring in another centre-half anyway.
"At the same time, it's not a long-term injury. We've just got to crack on and it gives someone an opportunity to come in and play - that's how we always look at injuries.
"If you pin all your hopes for a season on one player you haven't got a strong enough squad.
"When one door shuts, another one opens. It's very unfortunate for Zander but it gives an opportunity to either Marcus (Holness) or Phil (Edwards) and we're looking to strengthen in that area."