The Philadelphia Inquirer identified the white man as real estate developer Andrew Yaffe.
"What did they get called for, because there were two black guys sitting here to meet me," Yaffe says on the video. "What did they do? What did they do?"
"The police were called because these men hadn't ordered anything. They were waiting for a friend to show up, who did as they were taken out in handcuffs for doing nothing. All the other white ppl are wondering why it's never happened to us when we do the same thing," wrote Melissa DePino, who posted the video on Twitter.
The video has drawn more than 9.5 million views online, and there's an active #BoycottStarbucks hashtag on Twitter.
Many commenters on Twitter said Thursday's incident was reminiscent of the '60s lunch counter sit-ins that challenged Jim Crow laws, which were prohibited with passage of the Civil Rights Act of 1964. "This is a Jim Crow outrage," tweeted art instructor Rita Telaak.
Among the Philadelphia celebrities posting comments, Questlove, who is the drummer for The Roots, questioned the company's "practices and training," referenced in Starbucks CEO Johnson's statement. "10 times out of 9, if cops have to be called on black people it never ends in 'our bad ... have a nice day'." he tweeted.
Federal law says it is illegal for retailers to discriminate against customers by color, race, land of origin, religion or disability. However, retailers can refuse service based on a dress code, but the retailer must be consistent in applying that refusal.
In this case, Philadelphia Police Commissioner Richard Ross has defended the department's actions.
The officer and a supervisor did "absolutely nothing wrong," he said in a video posted on the Philadelphia Police Department's Facebook page. The men were released a short time later when Starbucks declined to prosecute, Ross said.
"As an African-American male, I am very aware of implicit bias," Ross said. "We are committed to fair and unbiased policing."
Police have not released the names of the men arrested.
Applebee's, IHOP, Old Navy
Starbucks is the latest retailer to face charges of discriminatory conduct.
Last month, Applebee's fired three employees after they were involved in the racial profiling of two African-American women who, while during their dinner at the Independence, Mo., restaurant, were falsely accused of skipping out without paying their bill the day before.
An IHOP in Auburn, Maine apologized after a server asked a group of black teens to pay upfront for their meal last month. The restaurant manager said he did not think the server's action was racially motivated because the restaurant had some problems with teens leaving without paying.
In January, a black man alleged that he had been racially profiled at an Old Navy store in West Des Moines, Iowa, when he was asked to prove he had previously purchased an Old Navy jacket he was wearing.
Celebrities say they've faced similar treatment. Actress Gabourey Sidibe wrote on the Lemmy Letter, an online feminist newsletter, how she had been racially profiled at a Chanel store.
Similarly, President Obama said he had been racially profiled prior to becoming president. "There are very few African-American men in this country who haven't had the experience of being followed when they were shopping in a department store," he said after the 2012 shooting of Trayvon Martin. "That includes me."
Starbucks CEO Johnson said the company planned to "investigate the pertinent facts and make any necessary changes to our practices that would help prevent such an occurrence from ever happening again."
Johnson said he would come to Philadelphia to "speak with partners, customers and community leaders as well as law enforcement. Most importantly, I hope to meet personally with the two men who were arrested to offer a face-to-face apology."
But some have questioned whether Starbucks fell short by not announcing immediate discipline for the store employees who called police.
"I'm tired of the continued racial profiling against communities of color, I'm tired of the weak corporate response when these incident(s) happen, & I'm tired of leaders standing by while disparate treatment of people of color makes headlines every single week," tweeted Kevin Johnson, a candidate for Pennsylvania's 3rd District in the U.S. House of Representatives.
In a subsequent tweet, Johnson said, "I applaud (district attorney) Larry Krasner for declining to prosecute these young men, and I am glad that Starbucks and the PPD recognize that there needs to be an investigation. We will not fix the problem if we continue to ignore the problem."
Actor-comedian Kevin Hart argued that it wasn't Starbucks the chain at fault, but the individual coffee shop. In a tweet directed at the local Starbucks, he said, "Message to the @Starbucks in Philadelphia. ...Our city is shining bright like a diamond right now," . Please make this situation right. I repeat please make this situation right!!!!!!! Once again MAKE THIS RIGHT"
A Starbucks boycott is not needed, Hart said. "The manager on duty was wrong," he tweeted. "That's who needs to take responsibility for this wrong doing."
Starbucks should look for appropriate short-term and long-term solutions to address this situation with a goal of preventing future ones, says Eric Dezenhall, co-founder and CEO of Washington crisis-management firm Dezenhall Resources.
Starbucks promises to look at racial profiling and "will need to address (that) … with internal guidelines, but big companies like Starbuck's understand something they will never communicate publicly: You have limited control over what a few of your ignorant employees do," he said.
The Associated Press contributed to this article.