Stankovich was sent off for a dangerous tackle on London Irish scrum-half Darren Allinson during last Sunday's LV= Cup game at Welford Road.
He was later cited for allegedly stamping or trampling on Irish's England international prop Alex Corbisiero in the same fixture.
The RFU announced that Stankovich pleaded guilty to both counts, and the offences were considered together in totalling up his period of suspension.
He cannot play again until December 12, which rules him out of Leicester's next three games - Aviva Premiership appointments with Wasps and Bath, plus a Heineken Cup tie against Treviso.
Worcester flanker Jake Abbott, meanwhile, was handed a two-week suspension by the same three-man panel.
Abbott was cited for a dangerous tackle on Scarlets player Kieran Murphy in an LV= Cup tie at Sixways 11 days ago. He admitted the charge.
He will be unavailable for Worcester's Premiership game at home to Saracens on Friday night, and a trip to league champions Harlequins seven days later.
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