Konerko had been expected to be available to come off the bench in Friday's 6-4 win against the Detroit Tigers, but never entered the game.
The nagging injury caused Konerko to leave the White Sox's May 7 win over the Seattle Mariners in the ninth inning. He said the next day that he has experienced chronic discomfort in the wrist for years, but that was the first time it happened during a game. X-rays on the wrist after that game appeared normal.
Konerko, who is hitting .310 with 12 home runs, has been the team's most consistent offensive threat all season.
Adam Dunn replaced Konerko at first base in Friday's starting lineup and batted seventh against Detroit left-hander Andrew Oliver. Dunn went 1 for 4, including an infield single off Tigers lefty Charlie Furbush -- Dunn's first hit against a left-hander this year. Dunn is hitting .182 with five home runs and 23 RBIs, and is now 1 for 42 against left-handers this season.
Sahadev Sharma is a regular contributor to ESPNChicago.com. Information from the Associated Press contributed to this report.