The running back, who hasn't played since Week 12, missed the Cardinals' past two games with a neck injury that didn't seem to be healing.
The Cardinals are 6-7 this year and will play the Redskins on Sunday.
Coach Bruce Arians said this week he wasn't sure whether Peterson would return from the injury and there had been no improvement in his condition. He had just 27 carries for 81 yards with New Orleans. He ran for 134 yards and two touchdowns on his Arizona debut, and racked up 314 rushing yards over his first three games, though he failed to rush for more than 79 yards over the next three games before injury struck.More news: This might be the creepiest viewership statistic Netflix has ever shared
Adrian's best game of the season came on November 5, rushing for 159 yards on 37 carries in a Cardinals' 20-10 victory over the San Francisco 49ers. He spent his first 10 seasons in Minnesota, becoming the franchise's all-time leader in rushing yards (11,747) and touchdowns (97).
With Peterson's roster spot vacant, the Cardinals added depth to the secondary, claiming Goodwin from the Atlanta Falcons.
It's also possible Peterson's incredible, Hall of Fame career will quietly end after a final season wearing two foreign uniforms. He entered the league with Pittsburgh as an undrafted rookie free agent in 2014 out of California University of Pennsylvania as a wide receiver and spent his rookie season on the Steelers practice squad.