Dunne, 32, came through the south London club's academy and made a total of 388 appearances for the Lions, scoring 23 goals.
Carlos Edwards, Ricardo Fuller, Danny Shittu and Martyn Woolford are among the 17 other players leaving The Den.
Harris will offer new deals to Jimmy Abdou and John Marquis.
On the departure of Dunne, Millwall chairman John Berylson told the club website: "It is always sad when a member of your family who has lived with you for a long time leaves home.
"He has written his own chapter in Millwall's history and he will always be very welcome whenever he returns.
"While Alan will continue his playing career elsewhere, it would not surprise me to see him back here in some capacity further down the line."
Senior players Nicky Bailey, Matthew Briggs, Richard Chaplow, Magaye Gueye, Justin Hoyte, Stefan Maierhofer and Angel Martinez have all been deemed surplus to requirements by Harris, who was appointed boss last week following a spell in interim charge.
Youngsters Dylan Casey, Sofiane El-Bekri, Denzel Gerrar, Jake Goodman, Josh Siafa and Callum Webb will also depart the club.
Edwards, 36, has been sidelined with a serious knee injury since September but has been offered the chance to continue his rehabilitation with the Lions.
Long-serving defender Alan Dunne is one of 18 players released by Millwall boss Neil Harris following their relegation from the Championship.