A father claims BA subjected him to "humiliation and racist behaviour", triggering calls for Indians to boycott the airline.
The father, an Indian civil servant called AP Pathak, has accused the airline of racism as he claimed a crew member threatened to throw his three-year-old son out of the window if he did not stop crying.
Mr Pathak said his family were offloaded, as well as another Indian family sitting behind them who had offered his son a biscuit.
British Airways said the family were repeatedly asked to sit their child down and fasten his seatbelt, as it was stopping the plane from taking off.
In a letter of complaint to India's aviation minister, Suresh Prabhu, Mr Pathak said he was subjected to "humiliation and racial behaviour" on the flight from London City to Berlin on 23 July.
Mr Pathak said his child started crying when placed in his seat before take-off so his wife took the child in her arms to comfort him.
He claimed a male crew member "started shouting and scolded my son" - and said his child was "terrified and started crying inconsolably".
As the aircraft started taxiing, Mr Pathak said: "The same crew member came again and shouted at my son that 'you keep quiet otherwise you will be thrown out of the window' and we would be offloaded.
Mr Pathak said the plane then returned to the terminal and security officers came onto the plane, took away their boarding cards and those of the Indian family behind them, then marched them off the aircraft.
In the letter, the civil servant added: "The crew member made racist remarks and used words like 'bloody' about Indians."
Indians on social media have called for a boycott of Britain's national carrier, with many calling the incident "shameful".
One man called on former Indian cricket captain Sachin Tendulkar and Bollywood legend Amitabh Bachchan to never travel on BA again.
But some were sympathetic towards the airline, with one person saying: "I don't feel bad about this at all, we Indians don't respect or value our Indian resources, be it trains or airplanes, this is good learning for us."
Vani M Manokaran said what BA did "was absolutely right", while Khushi said: "Indian parents start howling too when kids start howling - three-year-olds outside India are taught how to behave socially."
A British Airways spokesman told Sky News: "It is a safety requirement for all airlines that passengers are seated and have their seatbelt fastened for take-off.
"We are investigating the complaint and will liaise with our customer."