The video was taken at a staff meeting in Seattle in February, Business Insider said.
In the video, Schultz tells employees that there is "a tremendous amount of pressure and anxiety in America." He goes on to speculate that these feelings are hurting consumer behavior.
Schultz went on to tell employees that the coffee chain can provide "an antidote" by providing a "sense of community" to its customers.
Starbucks replied to a request for comment and confirmed the remarks captured.
"We can confirm that these comments were made by then-CEO Howard Schultz during a private meeting at the Starbucks Support Center in Seattle with our business leadership team on February 17," Starbucks said in an email to CNBC.
"It's important to note the timing of these comments, as they were made over three months ago and were centered around the sensitivity required for success in the retail business during that period of time. Also important to understand the full context for this comment as Howard also said: 'We have an antidote. We always have. And that's the sense of community, the third place, and the environment that we create around family.' "
The 63-year-old Schultz stepped down as Starbucks' CEO in early April, but remains the coffee chain's chairman.
Schultz has proclaimed himself a "life-long Democrat," and was an outspoken supporter of Hillary Clinton in her bid for the presidency.
Still, in December, Schultz told CNBC that he didn't think think the Starbucks brand was "at odds with the president-elect or his supporters."
He was also quick to criticize Trump's refugee policy earlier this year. Schultz, who was still CEO at the time, pledged in January to hire 10,000 refugees over the next five years after Trump's executive order suspended the U.S. refugee program and halted immigration from seven Muslim-majority countries. The federal courts have temporarily blocked Trump from enforcing that order.
This Starbucks policy sparked calls for a boycott when it was announced and it was the focus of criticism by some investors at the Starbucks' annual meeting in March.
Starbucks shares closed Tuesday essentially flat at $63.26. The stock is up nearly 14 percent in the year-to-date period, and has climbed nearly 15 percent over the past year.
—This story was updated with comment from Starbucks.