The London Irish star picked up the suspension for what was adjudged a dangerous tackle on Bath wing Tom Biggs last month.
Armitage must also serve a three-week ban for striking lock Dave Attwood with his knee in the same fixture, but that penalty will run concurrently.
He will be available to play again on December 9 as the ban is backdated to November 4, the date when London Irish suspended him following an internal hearing.
As a result the full-back will miss Heineken Cup meetings with Edinburgh and Cardiff Blues, plus Premiership assignments against Wasps and Saracens.
Explaining the decision reached by the RFU disciplinary panel, chairman Judge Jeff Blackett said: "We accept that both these incidents were reckless and not malicious. However, in relation to the dangerous tackle on Tom Biggs there was the potential for significant injury and for that reason we believe that it was a mid-range entry level offence of six weeks.
"We increased it to eight because of concerns raised by the IRB about injuries caused by dangerous tackles and because of his poor disciplinary record.
"We then reduced the sanction to five weeks because of his guilty plea, his contrition and the impressive way he conducted himself at the hearing.
"In relation to the strike to which he also pleaded guilty, we decided that this was a low-end entry offence and for that we imposed a three-week suspension."
The 27-year-old served an eight-week ban for pushing and verbally abusing an anti-doping official in a game on New Year's Day, and was then sidelined for another three weeks for a punch on Northampton fly-half Stephen Myler in April.
Armitage also missed England's World Cup quarter-final defeat to France for a high tackle on Scotland's Chris Paterson.
Meanwhile, the RFU also announced that the citing of Saracens' Owen Farrell for an alleged dangerous tackle on Gloucester's Henry Trinder had been dismissed, after the panel deemed there had been no act of foul play.
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