Seattle manager Scott Servais said Rodriguez jammed his wrist on a stolen base attempt against Texas on Sunday, and his status is day-to-day.
The Mariners announced moments before first pitch that the 21-year-old would not play as Seattle tried for its 15th consecutive victory, which would have matched the franchise record set in 2001.
Rodriguez was slated to hit leadoff and play center field in the Mariners' first game back from the All-Star Break. Dylan Moore made the start in center instead.
Rodriguez is days removed from a national coming out party at the All-Star Home Run Derby, where he lost to Juan Soto in the finals despite totaling a derby-most 81 home runs. He also played in his first All-Star Game on Tuesday.
He's a favorite for AL Rookie of the Year after hitting .275 with 16 home runs, 21 stolen bases, 52 RBIs and an .814 OPS during the season's first half.