Konerko, who has a loose ligament in his right thumb, left Wednesday's game after seven innings when the condition flared up. He was to get an injection and expected to be back Saturday "at the latest."
Konerko said he wouldn't rule out playing Friday in Milwaukee.
"It's no different than anything I had last year or in the past," he said. "I'm just trying to manage it to keep the pain down and sometimes it gets to where you can't do what you want to do out there. That's kind of where it's been the last couple days. But all in all, it's been pretty good this year.
"It's always going to be there. It's just a matter of managing it enough to where the discomfort is low enough to where it's not affecting the way I approach swinging the bat," he said.
Despite an 8-for-42 slump, Konerko was batting .291 with eight homers and 39 RBIs. He hit .240 while struggling through the thumb problem last year.
A shot during spring training helped, but Konerko started feeling some pain in Anaheim two weeks ago.
With an off-day coming on Monday, he was hoping to wait until Sunday for the injection, but the condition worsened. With Konerko out, Chicago manager Ozzie Guillen had the struggling Josh Fields starting at first base.