Armstead confirmed the news on Twitter, saying that he is symptom-free.
The Saints were scheduled to fly to Denver on Saturday. It was not immediately clear if anyone else's status would be affected due to contact tracing.
The Saints placed Armstead on reserve/COVID-19 list on Saturday.
The Saints will also be missing their starting left guard, Andrus Peat, because of a concussion -- not to mention quarterback Drew Brees, who is on injured reserve because of broken ribs and a punctured lung.
Armstead is a two-time Pro Bowler who was named second-team All-Pro in 2018.
He is now the second Saints player to test positive for COVID-19 during the season after WR Emmanuel Sanders missed two games earlier this year. RB Dwayne Washington also tested positive late in the preseason.