Saints confirmed on their website they had accepted the punishment offered by Scottish Football Association compliance officer Vincent Lunny earlier on Wednesday.
The left-back will now miss the Scottish Premiership derby against Dundee United on Monday night along with the last-four clash with Aberdeen at Easter Road on February 1.
Scobbie was accused of "violent conduct by headbutting or attempting to headbutt an opposing player, namely Brad McKay" after Lunny studied footage of the mass brawl which erupted after Hearts' late second goal during the 3-3 draw at McDiarmid Park on Saturday.
Scobbie went in goal after keeper Alan Mannus and Hearts forward Ryan Stevenson were sent off for their part in the melee and soon conceded an injury-time equaliser when Danny Wilson headed home.
Saints also had centre-back Steven Anderson sent off earlier in the game for a foul on Dale Carrick which referee Brian Colvin deemed to have denied the Hearts forward an obvious goalscoring opportunity.
But manager Tommy Wright confirmed the club would appeal against that decision in the hope that Anderson can face United.
Mannus missed the Perth club's 1-0 win over Partick Thistle on Tuesday night and will also sit out the Tannadice encounter but will be available for the semi-final.
Wright has been without another left-back, Brian Easton, for five games because of a hamstring injury but he could be fit for the Tayside derby.
The Saints boss lost Murray Davidson during the Hearts game to a serious knee injury which has ended the midfielder's season.