Muirhead hit out at the Doonhamers captain after seeing his penalty saved in the final minutes of extra time in the match, which was won by the the Dumfries club in a penalty shoot-out.
The 22-year-old was found guilty of breaching rule 201 of the SFA's judicial panel protocol, and a tribunal which met at Hampden on Thursday handed down the additional ban.
Muirhead had already received an automatic two-match ban for the act of violent conduct which, on top of an outstanding one-game suspension, ruled him out of Wednesday night's Irn-Bru First Division win over Morton.
A statement on Thistle's official website read: "An SFA disciplinary hearing today handed Aaron Muirhead an additional two-game ban following his red card against Queen of the South.
"The offence came with an automatic two-game ban which he will serve against Airdrie United and Raith Rovers.
"He will, however, also now sit out the games with Falkirk and Dunfermline Athletic before returning for the final game of the season at Dumbarton."
- Sports & Recreation