The men, who had not made a purchase, were handcuffed and arrested for trespassing on Thursday after a store manager called 911 and reported them for refusing to leave. Witnesses said the men were calmly sitting in the cafe and in a widely viewed video, some patrons asked police whether they were targeted because they are black.
Police released the men, who were not charged.
"The circumstances surrounding the incident and the outcome in our store on Thursday were reprehensible ... they were wrong," Johnson told ABC's Good Morning America on Monday, amid protests and calls for a boycott on social media.
The female manager who reported the men to police has left the company, a Starbucks representative said.
The incident came at a time when the company is grappling with flat traffic and lacklustre sales growth at its more than 14,000 U.S. cafes. It is a high-profile public relations test for Johnson, a former technology executive who took the helm at Starbucks roughly a year ago.
Representatives for the two men could not immediately be reached.
Protesters crowded the store that was the scene of the arrest on Monday morning. It was closed at around midday. More protests and a news conference are expected in the afternoon.
The Reverend Mark Tyler, part of an interfaith group organising a protest on Monday afternoon, said he had not heard reports of similar issues at other area Starbucks. Still, he said, "the idea of black people being unwanted in downtown Philadelphia is not new ... this is the underbelly of gentrification."
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)