Bradley left following an RBI single in the first inning Tuesday night.
Eric Byrnes replaced him in the field to start the second inning.
Bradley has been playing through a sore calf, knee and quadriceps muscle.
He singled in the first inning for his eighth RBI in eight games of the homestand.
He had started his debut season in Seattle 1-for-21 and lost his place as the Mariners' cleanup hitter. But he is 6-for-21 (.286) in his past eight games, including the single.
The often news-making Bradley is due in Chicago this weekend for the first time since the Cubs traded him this winter following one failed season. The Mariners and White Sox begin a three-game series Friday, and manager Don Wakamatsu expects Bradley to be in the lineup because "it doesn't look like anything serious."
Wakamatsu said he will rest Bradley in Wednesday's series finale.
Information from The Associated Press was used in this report.