The 27-year-old moved to Kingsmeadow in 2010 when Wimbledon were still in the Conference and has made 186 appearances, scoring 17 goals.
Moore came on as a substitute against Cheltenham on the final day of the season for his first appearance since the death of his mother a few weeks earlier.
Manager Neal Ardley told the club website: “We have had a difficult and emotional time with Sammy Moore lately.
“We had a really good heart to heart about his future. We both feel that a fresh start is probably needed so that he can get back to enjoying his football again, which is important after everything he has been through.
“It was a joint decision. I think it is going to be the best thing for him and what a fantastic servant that guy has been for this football club.”
Goalkeeper Ross Worner, defenders Mark Phillips and Jack Smith and winger Alfie Potter are also leaving at the end of their current contracts.
Full-back Callum Kennedy is in talks over a new deal and striker Adebayo Akinfenwa has been offered fresh terms.