Former Wales defender Edwards was only appointed as Ronnie Moore's full-time successor in May after the Merseyside club's relegation from League One.
However, he has been unable to reverse Tranmere's fortunes, with the club sitting bottom of League Two having accrued just nine points from 12 games and currently on a seven-game winless run.
And that poor form has prompted action from Tranmere chairman Mark Palios in an attempt to prevent the club from dropping out the league for the first time since 1921.
Palios told the club's official website: "Rob is a decent man who has worked very hard over the past few months for the Football Club.
"However, with the club currently sitting at the bottom of League 2 for the first time in 32 years it was decided this was the right time to make the break.
"I remain committed to the vision, that Rob shared, of playing free-flowing and skilful football.
"And while we have shown in some of our periods of play that we are not far off being able to achieve that - we have not been able to do it consistently.
"We have also not been sufficiently pragmatic when circumstances demanded that we close out a game to secure a win.
"If we are to achieve the required results in future it is clear that we need to strengthen the squad further."
