ESPN's Dianna Russini and Ed Werder first reported the news.
There had been hope throughout the week that Brees would be able to return this week. He told reporters Wednesday that "the plan" was for him to start against the Cardinals.
Brees came out clicking on all cylinders in a Week 1 victory over the Houston Texans, completing 32 of his 42 passes for 370 yards with two touchdowns and one interception.
The 40-year-old Purdue product suffered the thumb injury in the first quarter of the team's second game when his hand struck Los Angeles Rams lineman Aaron Donald on a follow-through.
Brees previously said the thumb likely wouldn't be back to full strength until around December but added that he wanted to play as soon as possible if his injury wasn't leading to mistakes.
"I mean listen, it's not fully healed I think until three months. But that internal brace obviously provides some stability and support, as does the splint," Brees told reporters.
On the topic of what would keep him sidelined, he added: "If I felt like, you know, hey, the ball is not coming out the way it needs to, right? Not as comfortable, not as confident, not as accurate. Those things will be factored."
Backup quarterback Teddy Bridgewater provided valuable stability under center during the longtime starter's absence. The former Minnesota Vikings star completed 67.7 percent of his throws for 1,370 yards with nine touchdowns and two interceptions across six appearances.
Getting Brees back still represents a major boost for the Saints offense, though. The 12-time Pro Bowl selection and two-time NFL Offensive Player of the Year is one of the most decorated signal-callers in history and looked primed for another massive statistical season before the injury.
His return should push New Orleans, which owns a 6-1 record despite his absence, toward the forefront of the championship conversation during the season's second half and into the playoffs.