Black tells the fan to sit down three times before shoving him.
"Officer, that is abuse," Buck says as he bounces back to his feet.
Black then shoves Buck two more times.
Commander Matt Murray, the department's chief of staff, declined to release details of the incident, including what led to the confrontation and whether the man was charged with any crime.
"We're investigating and that's it," Murray said.
On Thursday night, the police department sent out three tweets assuring the community that the incident was being taken seriously.
Jay Alves, the Rockies vice president of communications, referred questions about the incident to Denver police.
Black, who commands the department's juvenile division, was working off-duty security during the baseball game, Murray said.
In the video, Buck tells the officer he is 22-years-old and had three beers. He also repeatedly yells that the officer is violating the rights of an "American citizen."
At one point, Buck tells the officer, "Abuse me again. As a citizen of the United States of American, abuse me again."
Friends of Buck, who are not seen on camera, are heard telling him to quit talking before he causes himself more trouble.
Buck told The Denver Post via a Facebook message that he had not been arrested or charged after the incident. He said he was ejected from the ball park.
The video had been shared more than 21,000 times shortly before 6 p.m. Thursday. Murray said people have been posting links to it on the department's Facebook page.
Denver police have contacted Buck as part of the investigation, Murray said.
"We care about this," he said. "We're going to do the right thing."
Noelle Phillips: 303-954-1661, firstname.lastname@example.org or twitter.com/Noelle_Phillips
Click here to see the video.