The move comes with veteran infielder Jhonny Peralta set to come off the disabled list Tuesday. Peralta had surgery in March to repair ligament damage to his left thumb.
St. Louis general manager John Mozeliak said last week that Wong could be without an everyday job when Peralta returned. Hot-hitting rookie Aledmys Diaz is set to remain at shortstop, with Peralta shifting to third, and Matt Carpenter getting the bulk of his playing time at second base.
Wong, 25, is batting .222 with a .571 OPS and six errors this season.
"The key is to get everyday at bats," Mozeliak told ESPN on Monday. "And given our current roster it would be hard to do."
Wong batted .262 with 11 home runs and 15 stolen bases last season.
He inked an extension in March that includes a $12.5 million team option for 2021 but does not have any no-trade protection.
Information from ESPN.com's Mark Saxon was used in this report.