In November, the Lions made the decision to appoint the former Chelsea and Everton assistant as the successor to Gary Rowett.
When Edwards' reign began with a 4-0 victory away at Sheffield Wednesday, there was immediate justification for what had been a surprise managerial change.
However, Millwall would win just three of Edwards's following 18 games, all in succession over the Christmas and New Year period.
Since then, the East Londoners have lost seven of eight matches in all competitions, including the last four which has included a 4-0 home reverse to Ipswich Town and 2-0 defeat versus Sheffield Wednesday at The Den.
As a result, Millwall now sit just one point above the Championship relegation zone, leading to the club's hierarchy to make a further change in the dugout.
Chairman James Berylson said: "This has of course been a very tough time and it is not a decision that we have taken lightly.
"Joe has worked incredibly hard during his spell with us and it is with sincere regret that the move hasn't worked out for both parties in the way we had anticipated.
"I cannot praise him highly enough for his professionalism, standards, values, and work ethic, and I am confident he will have a long and successful career as a Head Coach.
"I would like to thank Joe and Andy for everything they've done for the club and wish them every success for the future."
Reports on Wednesday have suggested that Millwall are attempting to secure a reunion with former boss and club legend Neil Harris, who is currently in charge of League One outfit Cambridge United.