The midfielders was sent off for an incident involving himself and Matt Derbyshire, the striker who spent part of last season on loan at Wrexham.
Tranmere went on to lose the game 7-0.
As the fixture list currently stands, Harrison will miss the games against Blackpool (24/11/06), Scunthorpe (5.12.06) and Brentford (9.12.06), but should Rovers be called into action in the F.A. Cup 2nd Round or be involved in an F.A. Cup Replay, the midfielder will also miss these games.