Wise will be out of action for at least six weeks, by Ozzie Guillen's estimation, after suffering the injury while making a game-saving, tumbling catch in the fifth inning of Monday's 10-6 victory.
And as far as Anderson's hold in the middle of the outfield is concerned -- a full-time position he has wanted a chance at for the past two years, although not at the expense of his friend and teammate -- the definition of foreseeable completely depends on how Anderson performs.
"Brian Anderson will dictate how much he's going to play," the White Sox manager said. "The leash, I don't want to say it's short or it's long. I want to see how many good at-bats he's going to give me.
"He might have another chance to be back in the big leagues and play every day. We need whoever plays to step it up and play good, but I don't expect Brian to hit .350."
Guillen does expect Anderson to play his usual stellar defense in center, where he ranks as one of the American League's best outfielders with the glove. Anderson also has been talked about as possessing the potential to hit 20-to-25 home runs when given consistent at-bats, but Guillen isn't worried about such flash.
If Anderson can produce quality at-bats like the two walks he drew after replacing Wise on Monday, followed by a stolen base on each occasion, then Anderson might hang on to the job for the duration of Wise's absence. If those quality at-bats don't exist, general manager Ken Williams might have to go outside the organization to find a replacement.
"Well, I'm not going to stay outside. But this ballclub has a chance to win and we are going to do the best we can to have the best ballclub on the field," Guillen said. "We had a brief conversation about it, and we might sit down tomorrow and look at the real scenario.
"You can dream and have your fantasy camp, your fantasy games. We have to sit down and talk about what's best for the ballclub. How long is this kid going to be out and what we need? If Kenny sees it that way, then he will make a move to help this ballclub.
"A lot of people forgot we give Brian all year long [in 2006] and he never took ... ," said Guillen, before traveling down another road concerning Anderson. "Right now, he's mature, he's a better player and he knows what he does. I don't expect him to be comfortable with being a backup outfielder. He should be better than that. He has an opportunity and we'll see how he handles it."
Jerry Owens' contract was purchased from Triple-A Charlotte to take Wise's roster spot. It has been a long, strange trip for Owens, dating back to 2007, when he established himself as a viable leadoff presence during a down season for the team.
That successful run was hampered by a groin injury in Spring Training 2008 and then less-than-stellar play during the White Sox first spring in Phoenix, starting this past February. Owens cleared waivers after losing the center-field battle to Wise and Anderson and was outrighted to Charlotte.
Losing that spot on the 40-man-roster served as a bit of a wakeup call for the 28-year-old.
"Honestly, getting taken off the roster and getting sent to Charlotte was a blessing for me mentally because you can get comfortable on the 40-man," said Owens, during a direct and honest conversation with the media Tuesday. "You're a prospect, you're going to be playing every day and sometimes you take it for granted.
"I lost sight of what I bring to the table as far as being a leadoff hitter and an igniter. Just in the past 10-12 days, I've been able to sit back and realize what I have to offer to the Chicago White Sox."
Part of the spring problem for Owens was that he didn't show the energy desired by the White Sox at the top of the order. Owens' low-key personality won't change, but the fleet-footed left-handed hitter now realizes he just needs to play, instead of thinking about what he could be. It's a school of thought Anderson will try to follow as well.
"When I was at my best, I didn't think about how to get to that. I just got to that," Owens said. "So that said something to me in my head, to go out and play and have fun and lay it all on the field. That's one thing I've learned about playing for Ozzie is the only thing he wants is to play hard. I can control that. Instead of thinking about who to be, I just need to go be, so to speak."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.