Muirhead hit out after seeing his penalty saved in the final minutes of extra time in the match, which was won by Queens 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 yesterday handed down the additional ban.
A statement on Thistle’s website read: “An SFA disciplinary hearing 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.”
An outstanding suspension meant Muirhead missed Wednesday’s win over Morton.