The incident, which happened on a Ryanair flight from Barcelona to London on Friday, was filmed by another shocked passenger.
In a shocking video captured by fellow passenger David Lawrence, a man can be heard referring to the pensioner as an "ugly black bastard".
The elderly woman was later named as Delsie Gayle.
Scores of commenters expressed outrage over how the matter was handled and demanded to know why Ryanair's flight crew didn't remove the male passenger before the plane took off. Gayle then leaves her seat and walks toward the back of the plane. He may now get away with it.
A flight attendant told the man he needed to calm down, and asked Mrs Gayle if she wanted to move to another seat.
"He continually threatened physical violence and racial slurs and RYANAIR did nothing!" Mr Lawrence later uploaded the video to YouTube, where it has more than 100,000 views.
Ryanair is under fire for not removing the man from the flight.
The transport secretary, Chris Grayling, described the incident as "totally unacceptable" and told the Today programme he hoped "police would want to take action in such an extraordinarily unacceptable case". He chose to upload the video out of frustration for the situation, and felt people needed to know what happened.
The clip shows the daughter of the elderly woman engaged in an argument with the man, who then starts verbally attacking the 77-year-old.
The woman, who has been identified by her daughter as Mrs. Gayle, is a Windrush generation Jamaican migrant who was returning from a holiday to mark the anniversary of her husband's death.
The footage shows a man shouting at a woman in his row, telling her to move seats, while her daughter tries to stand up to him, telling him her mother is disabled.
He says: "I don't care whether she's f****** disabled or not - if I tell her to get out she gets out".
At one stage, Gayle herself asks to be moved and can be heard telling the man he stinks and needs a wash.
Gayle adds that the airline has not contacted her.
Ryanair, however, has told the Post that it will be "taking this matter further" by banning passengers who exhibit disruptive or abusive behavior. "I'll tell you this", he told her. "If you don't go to another seat, I'll put you into another seat".
Speaking about how the abuse has affected her, she told ITV: "I feel very low".
Questions have been raised over the capability of Ryanair's cabin crew to deal with situations involving abusive passengers.