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.

A 30ft (9m) decomposed whale washed up on the beach at Felixstowe on Sunday and the body of a minke whale was spotted near Orford on Saturday.
Scientists from the Cetaceans Strandings Investigation Programme (CSIP) say there is now a third dead whale off the coast.
They do not think the deaths are linked.
The third whale floating off the Suffolk coast is thought to be a sperm whale, Rob Deaville, from CSIP, said.
More on this and other news from Suffolk
He believes the whale on the beach at Felixstowe is a fin whale and a large injury on its body is the result of it being struck by a vessel "some time ago, perhaps hundreds of miles away".
CSIP - which attends cases of whales, porpoises and dolphins that become stranded on the UK coastline - is currently examining the Felixstowe whale.
It is too decomposed to carry out a full post-mortem test but samples have been taken to assist with analysis in terms of whale population, Mr Deaville said.
The Orford whale stranded on mud flats on the tidal River Ore will be "tricky to get to", Mr Deaville said.
However, he does not believe the deaths are in any way related.
"Three very different species, and in my opinion, they're not linked," he said.
"It's a series of coincidental events.
"We see hundreds of strandings a year, it just happens that these three are in close proximity."
A spokeswoman for Suffolk Coastal and Waveney Councils said contractors were expected to remove the whale from the beach at Felixstowe on Wednesday.
It is not yet known when the body of the Orford whale will be moved.
Wigan prop Ben Flower has been given a two-match ban for a "reckless" elbow against Warrington's Declan Patton.
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A third dead whale has been found by experts investigating the deaths of two others found along the Suffolk coast.