It was not known what symptoms Benson, 73, has displayed since contracting the deadly virus within the past few weeks.
"Mrs. Benson did test positive for COVID-19," the Saints said in a statement. "She is progressing well and improving daily.
"She has not missed a daily work call with the Saints and Pelicans staff nor has she missed an NBA or NFL owner call in recent days -- she was not hospitalized and is recovering at home in New Orleans."
New Orleans Saints coach Sean Payton was diagnosed with COVID-19 in March, the first NFL coach known to have contracted the coronavirus.
The team is set to open its 2020 NFL season on September 13 at home against the Tom Brady-led Tampa Bay Buccaneers.
The Pelicans, sparked by rookie star Zion Williamson, finished their 2019-20 NBA season earlier this month, going 2-6 in the COVID-19 quarantine bubble at Disney World in Orlando, Florida, to finish the campaign 30-42, 13th in the Western Conference.