In the 30-second video, which begins and ends in the middle of the incident, a woman who identifies herself as Ashley tells the man recording on his cell phone: "I'm getting into a fight with some Muslim chick because she has an attitude. She thinks she has rights that she doesn't have."
It's not clear from the video what sparked the altercation.
Marco Lao, who posted the video to Twitter and YouTube on Tuesday, said the woman in the head scarf had trouble getting her stroller on the bus and the other woman yelled at her.
The two argued, he said, but Lao found it hard to hear what the woman with the stroller was saying.
The screaming woman began to spew Muslim stereotypes, and told the woman in the head scarf that "ICE should take her kids away," he said.
Lao said he thinks at one point the Muslim woman told Ashley, "You're an immigrant, too."
After he began recording, Ashley yelled at the woman, claiming she is not a citizen and cannot speak English. The woman says something that cannot be understood from the recording.
"Immigration at the door," Ashley yells. "Oh wait, is that ICE? Oh, mama, they here for you."
The video ends abruptly, but, according to Lao, the bus driver intervened over the intercom and the situation was defused.
He said the Metropolitan Transportation Authority bus was headed from Manhattan to Staten Island. The New York Police Department said they had no information on the incident. The MTA said they are aware of the video and are looking into it.
Lao said he doesn't know either of the two women involved.