The incident occurred as Seattle police were responding to an armed robbery call near a nightclub in Seattle's Westlake neighborhood on April 17. Patrons had called police and described the suspects as Hispanic.
The video -- shot by a freelance videographer and aired Thursday by KIRO -- shows a group of officers surrounding two men lying on the ground.
At one point, an officer approaches one of the men and can be heard saying: "You got me? I'm going to beat the (expletive) Mexican (expletive) out of you homey. You feel me?"
Soon after, officers kick the man in the head, hand and leg.
It turned out the man was not the robbery suspect, and the officers let him go.
A tearful Detective Shandy Cobane told reporters the words he used "were offensive and unprofessional."
"A day has not passed that I wished I could rewind the events of that night and take back those hateful words," he added.
Cobane apologized to the Latino community, saying, "I know that my words cut deep and were very hurtful."
"Please know that I am truly, truly sorry," the officer said.
He also apologized to Interim Police Chief John Diaz and his fellow officers.
Diaz said it was Cobane's decision to offer a public apology. The chief adds an internal investigation will continue.
"I watched the video and found it disturbing," Seattle Mayor Mike McGinn said earlier in a statement, adding he has spoken with Diaz.
Cobane and a female officer seen in the video are both on administrative leave.
In a statement, police said the internal investigation of possible officer misconduct was being handled by the Office of Professional Accountability.
The video shows the unidentified man gingerly getting up after being on the ground. The man is approached by the videographer and asked why he was kicked.
"I don't know. They knocked me down and kicked me in the head," the man responds.