The Chiefs placed Nelson on their injured reserve list Sunday. He can begin practicing with the Chiefs after six weeks and begin playing in games after eight weeks.
"He had the problem through training camp,'' trainer Rick Burkholder said. "He tried to fight through ... He got through three preseason games and just felt like he couldn't play up to speed.''
The Chiefs replaced Nelson on their roster by re-signing running back C.J. Spiller, who was released on Saturday in the cut to 53 players. By rule, a player can return from injured reserve only if he is on a team's initial 53-man roster.
Nelson started 14 games for the Chiefs last season plus their playoff loss to the Pittsburgh Steelers.
The Chiefs, who have Marcus Peters as one regular cornerback, can choose between Phillip Gaines and Terrance Mitchell as Nelson's replacement. Gaines has started 13 games over three seasons with the Chiefs. Mitchell joined the Chiefs last year and played well as their third cornerback for the last half of the season.