TMZ broke the story ... cops issued an arrest warrant for Cuba following the incident at The Old Absinthe House on Bourbon Street early Tuesday morning -- when the bartender said Cuba shoved her for telling him to leave the pub.

According to the bartender, Cuba was intoxicated and had gotten angry at other bar patrons for taking pictures of him ... at which point, she told Cuba to get lost. That's when she says Cuba roughed her up.

The video cuts in right after Cuba leaves the bar, and the brunette follows him into the street, telling someone to "call the cops right now."

Cuba tells onlookers, "She's racist. She's racist. She doesn't like me." Moments later, another bystander yells, "He took a woman and he shoved her!"