The incident took place when the woman boarded the flight from San Francisco to Dallas yesterday.
In a video posted on Facebook by Surian Adyanthaya, the employee of the Texas-headquartered American Airlines (AA) can be seen arguing with a passenger on board the flight.
The footage does not catch the moment when the flight attendant allegedly struck the woman, but the atmosphere in the cabin gets tense as a man steps in to defend her, New York Daily News reported.
"Hey bud, you do that to me and I will knock you flat," the man says to the attendant as the distraught woman stands to the side clutching her baby, with tears streaming down her face, the report said.
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"You stay out of this," the attendant shouts.
The man then takes a step forward and the attendant immediately turns confrontational.
"Hit me, c'mon, bring it on!. C'mon, you don't know what the story is," the employee says.
The woman was eventually escorted off the flight, but the quarrelsome attendant is allowed back on.
The video has gone viral on the social media with more than 3,500 shares.
AA condemned the flight attendant's behaviour and said it had launched an investigation into the incident, the report said.
"What we see on this video does not reflect our values or how we care for our customers. We are deeply sorry for the pain we have caused this passenger and her family and to any other customers affected by the incident," the airline said in a statement.
"We are disappointed by these actions," it said.
The incident comes weeks after a Vietnam-origin doctor was dragged and beaten up by police officers on board a United Airlines flight at Chicago international airport after he refused to give up his seat to an airline employee who needed to catch a connecting flight.