Rhodes has a broken bone in his left foot and coach Ken Whisenhunt acknowledged Monday that the safety would be sidelined for several weeks but said only that surgery might be necessary.
Rhodes was injured early in Arizona's 34-10 loss at Minnesota. Rashad Johnson will move into Rhodes' free safety spot.
"(It) is a shame, because Kerry had been playing good football for us," Whisenhunt said, according to the Arizona Republic.
The 29-year-old Rhodes has 24 tackles and two sacks in five games this season.
Information from The Associated Press was used in this report.