Authorities have identified the woman in the video, they said, but haven’t released her name.
Following the Pennsylvania State Police investigation, the Allegheny County District Attorney’s Office will review its findings.
The second lady caught a few seconds of the parking lot portion of the encounter on video and posted it to Twitter.
“It was a hard reminder for me that it doesn’t matter what I’ve overcome, what I’ve achieved, that to some I will always be viewed as inferior simply because I was not born in this country,” she told CNN.
The woman under investigation is no longer welcome in Aldi stories, the company said in a statement.
“We absolutely do not tolerate harassment, discrimination or mistreatment of our customers or employees, and we condemn it in all forms,” it said. “We are reaching out to the Second Lady today to reiterate our stance, and ensure she feels safe and welcome in our stores anytime.”
Fetterman met then-Braddock Mayor John Fetterman in 2007, and they married the following year. They have three children.
Since moving to Pennsylvania, Gisele Fetterman has developed a deep record of helping others, including the impoverished, immigrants, LGBT, minorities, imprisoned and the hungry. She’s earned myriad awards for her philanthropy.