The video begins with a shot of that woman before turning to the victim, who is seated in the corner of a room with his mouth covered. The woman laughs as two men cut the sleeve of the victim’s shirt. One of the men yells epithets about Mr. Trump and “white people.” Later, a man cuts a patch of hair from the victim’s head, appearing to draw blood in the process.

Mr. Johnson said criminal charges against the suspects, two men and two women, could be announced on Thursday. Investigators said they were not yet sure of a motive, but could pursue hate crime and kidnapping charges if the evidence warranted. The victim knew one of his attackers, the police said, and had been taken from the suburbs to the city and held for some time before the beating was streamed online.

“Images in the video put on display the brazenness of the offenders who assaulted the victim and then broadcast it for the entire world to see,” Mr. Johnson said.

The victim, whom the police did not name, was hospitalized for undisclosed injuries, but had been released by Wednesday evening and was speaking with investigators. The police said he was “traumatized” and initially had trouble communicating with detectives.

The video’s spread online comes at a time of relentless violence in Chicago. In a Twitter post this week, Mr. Trump cited Chicago’s 762 murders last year and suggested that the city should seek federal help if local efforts to control the violence continued to be ineffective. Superintendent Johnson declined to speculate on whether the president-elect’s Twitter message and the videotaped beating were connected.