Argyle have won just one of their last 13 league matches and have slipped deep into relegation trouble.
Tuesday's opponents Rovers - who are second from bottom in the table - are now just two points adrift of Plymouth with two games in hand.
A statement on the club's website read: "The team's recent results have not been good enough and, with the club's Football League future paramount, the Argyle Board felt that a change was necessary now as we head into an important part of the season.
"The owner and the Board would like to thank Carl for all he has done for the club, as a player and a manager.
"Carl helped keep us in the Football League last season and we will never forget that huge contribution he made to Argyle's history.
"He leaves with our best wishes for his future career and will always be welcome at Home Park.
"The Board will now seek promptly to appoint a new manager. The club will be making no further immediate comment to this announcement."