The Patriots said Cunningham would begin serving his ban immediately after testing positive for performance-enhancing substances.
He will be eligible to return to the active roster on Dec. 24.
The third-year player has logged 23 tackles and 2 1/2 sacks while appearing in all 11 New England games this season.
The Patriots this month also suspended running back Brandon Bolden for four games after a test for a banned substance.
Celebrity Families of 2014 [PHOTOS]