This is the Ducks' 10th team award in the award's 11-year existence.
The Women of Oregon scored 34 points, four shy of a top-four podium finish.
The Men of Oregon finished tied for 12th at the national meet with 23 points.
The Women of Oregon scored 10 points and secured four finalists on day two of the NCAA Championships.
Oregon has six scoring opportunities remaining at the NCAA Championships in Austin.
Oregon will cap its 2019 season at the NCAA Championships (June 5-8) in Austin, Texas.