The Chiefs declared Edwards-Helaire out for the game on Saturday and said he did not travel with the team to Cincinnati.
Edwards-Helaire, who leads the Chiefs with 517 rushing yards, injured a shoulder in last week's victory over the Pittsburgh Steelers and did not practice all week.
ESPN's Adam Schefter reported earlier this week that Edwards-Helaire is considered week-to-week with a bruised shoulder.
The Chiefs activated running back Jerick McKinnon off injured reserve and he will be available to play against the Bengals. McKinnon had been on injured reserve with a hamstring injury.
The Chiefs will also have Darrel Williams and Derrick Gore available at running back on Sunday. Williams is the Chiefs' second-leading rusher with 453 yards. Williams is also fourth on the Chiefs with 41 receptions.
Gore was elevated from the practice squad early in the season. He has 189 rushing yards.