Under the suspension, neither player will be available to practice this week or to play in the Jags' next game against the Vikings on Saturday.
Ramsey played briefly in Jacksonville's preseason opener against the New Orleans Saints on Thursday. Fowler was just activated from the physically unable to perform list on Saturday.
NFL Network Insider Ian Rapoport reported Ramsey's suspension was a direct result of the cornerback going after a local reporter on Twitter on Sunday.
Ramsey issued this tweet in response to the suspension: