Nelson, a defensive captain, suffered the injury Saturday in Oklahoma's 20-17 win over TCU. Coach Bob Stoops said the procedure would take place Tuesday.
Nelson's 27 tackles are second-most on the Sooners, who play Texas on Saturday. Nelson also returned an interception for a touchdown on the opening series of Oklahoma's win at Notre Dame two weeks ago.
The Sooners, who struggled defensively last season, currently have the No. 1 defense in the Big 12.