This is the 23-year-old's second punishment for breaking the league's rules, as last year he was banned for four matches in his rookie year for the same reason.
Head coach John Harbaugh told reporters: "If you don't follow the rules, you get suspended. That's a fair rule, there's no place for that, and he's getting what he deserves.
"As far as what it does to our corner depth, that's one less corner that we have. We'll be missing Asa those first eight weeks. Whether he'll back after that, time will tell."
Jackson was drafted in the fifth round of the 2012 draft.