The 26-year-old Donahue pleaded guilty last month to charges in two separate incidents in which he was arrested for driving while intoxicated.
Police said he caused a wrong-way crash in February that injured four people in New Jersey. He also received a three-month suspended sentence and was fined $1,000 for a DUI crash in his hometown of Billings, Montana, in May 2017.
Donahue was among the Jets' final roster cuts two weeks ago and is currently a free agent.
Howard Balzer of BalzerFootball.com first reported the league's punishment Friday.
Donahue spent a month in a substance-abuse treatment facility in Florida shortly after crash in the Lincoln Tunnel in February. He told reporters last month that he hadn't had alcohol since.
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