It means the Wales international is free to play in the Grand Final should Wigan make this season's showpiece.
Flower, sent off in the first minute of the 2014 Grand Final against St Helens and subsequently banned for six months, will miss the final Super Eights game against Catalans and the semi-final.
A disciplinary panel also fined the 28-year-old £300 for the grade C offence.
In its findings the panel said it accepted Flower's elbow had not been deliberate but added: "This was a reckless act that had contact with the opponent's head and with obvious risk of serious injury."
Despite the loss of Flower, the Warriors went on to win the game Halliwell Jones Stadium 35-28.
It was the first time he had been dismissed since receiving the longest ban in Super League history for punching St Helens' Lance Hohaia two years ago.
Wigan have already secured a play-off semi-final place and could yet win the League Leaders' Shield.
Wigan prop Ben Flower has been given a two-match ban for a "reckless" elbow against Warrington's Declan Patton.