Jackson, drafted in the fifth round last year, was given a four-game suspension during the 2012 season. He will not be eligible to play this year until Nov. 10 against Cincinnati.
He issued a statement to the Baltimore Sun that said he had been diagnosed with a condition that could be treated with a medication that is banned by the NFL. Jackson said he received approval to take the medication, but that the approval came after he had failed a drug test.
"You've got to follow the rules," Baltimore Coach John Harbaugh said on the team's website. "There's really no place for that. He's getting what he deserves. We'll be missing Asa for the first eight weeks. Whether he'll be back after that, time will tell."