Armstead suffered the shoulder injury on Wednesday, according to NFL.com.
"Heartbroken when I found out I need surgery! No one is more frustrated than me after working so hard," Armstead tweeted. "I'll be back #WhoDatNation STRONGER!!"
Saints coach Sean Payton was asked about losing the blindside protector at Thursday's press conference.
"Right now there's nothing to report and, you know," Payton told reporters. "I'm not going to talk about an injury until September 11. You'll get the status [that week.]"
Armstead signed a five-year, $65.25 million contract extension during the 2016 offseason. He missed nine games last season due to injury. The Saints drafted tackle Ryan Ramczyk with the No. 32 overall pick in the 2017 NFL Draft.
Heartbroken when I found out I need surgery! No one is more frustrated than me after working so hard. I'll be back #WhoDatNation STRONGER!!— Terron Armstead (@T_Armstead72) June 16, 2017
Saints center Max Unger had foot surgery in May but is aiming for a Week 1 return, according to the New Orleans Times-Picayune. Armstead's surgery is scheduled for Monday. Ramczyk is one option to fill Armstead's place if the team doesn't decide to move left guard Andrus Peat over to tackle. The Saints also re-signed tackle Khalif Barnes in May.
Armstead welcomed his newborn son, Tristan Truth Armstead, in May.