Reds manager Bryan Price said Hamilton suffered the injury while sliding into second base on a stolen-base attempt in Friday night's loss to the Mets.
Hamilton, who is hitless in his first 12 at-bats this season, is considered day to day. Roger Bernadina will start in center field and bat leadoff Saturday.
After striking out six times over the first three games of the season, Hamilton came off the bench as a pinch runner Friday and was caught stealing in the eighth inning. It marked just the second time in his brief career that Hamilton was caught stealing.
The Reds are counting on the speedy Hamilton to have a productive first full season in the majors. He had 13 stolen bases in 13 games last year and began this season as Cincinnati's replacement atop the order for Shin-Soo Choo, who signed a lucrative offseason contract with the Texas Rangers.
Hamilton, 23, set a professional record by swiping 155 bases in 2012 at Single-A and Double-A.
ESPNNewYork.com's Adam Rubin and The Associated Press contributed to this report.