The Serbia international had been hopeful of having overturned the dismissal by referee Stuart Attwell for a challenge on Gunners midfield Mikel Arteta during the second half of the 1-1 draw.
But a Football Association disciplinary committee have dismissed his appeal and his ban will begin with Saturday's Barclays Premier League bottom four clash at Bolton.
Milijas will also be ruled out for the home league game with Chelsea on January 2 and the FA Cup third-round tie with Birmingham at St Andrew's five days later.
Wolves boss Mick McCarthy is to make no comment on the FA decision until his media conference ahead of the Bolton game.
But he was seething immediately after the game at Emirates Stadium.
When asked if he thought Milijas' challenge deserved a sending-off, McCarthy said: "I will go and ask Stuart (Attwell). He did what he saw but if he sees it again, then he will know that it can't be one (a red card).
"Nenad has got his foot on the ground, makes contact with the ball and I don't think he leaves the ground.
"Someone said to me that his studs were up. Well you generally do when you tackle with your foot, sliding in."
Source: PA
Source: PA