Jay is expected to rejoin the team Friday in Arizona when the Cardinals face the Diamondbacks. The Cardinals do not play Thursday.
Jay, who had an RBI in Tuesday's loss to the Cubs, is batting .302 with 52 runs in 138 games this season.
The Cardinals currently lead the Pittsburgh Pirates by 1 1-2 games in the NL Central.
Peter Bourjos will start in centerfield in Jay's absence.