Jon Heyman of the MLB Network reported the update Tuesday and noted the typical recovery timeline for the injury is three-to-four weeks.
Stanton, who was limited to 18 appearances last season because of biceps, shoulder and knee injuries, was off to a red-hot start before the latest setback.
The 30-year-old California native posted a 1.038 OPS, which ranks 12th in MLB, with three home runs in 14 games.
He suffered the hamstring injury during Saturday's game against the Tampa Bay Rays.
"[I'm] hurting for him, period," Yanks manager Aaron Boone told reporters. "I know what he's done to be here. I know obviously his play speaks for itself. So hopefully it's something that doesn't end up keeping him down too long."
Stanton had operated exclusively as the club's designated hitter in the early stages of the coronavirus-shortened 2020 season.
Mike Ford should receive most of the additional playing time during the slugger's absence. It could also lead to a few extra starts for Mike Tauchman and Tyler Wade.
A monthlong stint on the injured list would give Stanton about two weeks to get back up to full speed before the playoffs.
The Yankees are back in action Tuesday night when they open a two-game home series against the Atlanta Braves at Yankee Stadium.