Right-back Neal Eardley, 28, and midfielders Paul Anderson, 28, and 21-year-old Emmanuel Sonupe are also leaving the club.
Diamond's fellow centre-back Gabriel Zakuani has been offered a new contract but four others have been transfer listed.
They are Jak McCourt, Harry Beautyman, Raheem Hanley and Rod McDonald.
Centre-back Diamond, 32, and Smith, 24, were both part of the side that won the 2015-16 League Two title.
Smith, who played 40 of Northampton's 46 games as they finished 16th in League One this term, pre-empted the club's official announcement by taking to Twitter to inform supporters he would be leaving.
"I will be moving on next season," Smith tweeted. "I have grown as a goalkeeper and as a person whilst being at this great club."
Player of the year Zander Diamond and goalkeeper Adam Smith are among five players to be released by Northampton.