Flannery, who was chosen to tour with the 2009 Lions before injury prevented him from travelling to South Africa, was handed the ban for kicking France wing Alexis Pallison during Ireland's Six Nations defeat in Paris on February 13.
The 31-year-old pleaded guilty to the offence at a disciplinary hearing but later lodged an appeal against the length of his suspension.
An independent appeal committee, chaired by Judge Jeff Blackett, the disciplinary chief of England's Rugby Football Union and also consisting of Italy's Marco Cordelli and Douglas Hunter of Scotland, upheld the length of the ban, although they chose not to increase the suspension despite a separate plea to do so from the Six Nations disciplinary officer.
The result of the appeal means that Flannery remains suspended until March 29.
He will therefore miss the remainder of Ireland's defence of their Six Nations crown, as well as three more Magners League games.
Flannery will be unavailable for the March 13 clash with Wales and the following week's encounter with Scotland, in addition to Munster's league ties with the Dragons, Scarlets and Glasgow Warriors.
He could return for the Magners League derby with Leinster on April 2, a week before Munster host Northampton in the last eight of the Heineken Cup.