The 31-year-old, who was selected in the original Lions squad for the 2009 summer tour before injury prevented him from travelling to South Africa, pleaded guilty to kicking France wing Alexis Palisson during Ireland's 33-10 defeat in Paris last Saturday.
Flannery himself acknowledged that the 23rd-minute incident deserved a red card despite referee Wayne Barnes only awarding a penalty at the time.
The ban rules Flannery out of his country's clashes with England, Wales and Scotland, as well as Munster's Magners League games with Edinburgh, the Dragons and league leaders Glasgow.
Flannery's ban runs until March 29, meaning his comeback game is likely to be the mouthwatering Magners League tie with Irish rivals Leinster at Thomond Park on the weekend of April 2.
Flannery, who could have been banned for up to a year, has the right of appeal, with the minimum punishment for the offence being four weeks.
The Irish Rugby Football Union has stated it will wait until it receives the full written judgement before deciding whether or not to attempt to have the ban reduced.