Balpa said it was told about the proposed job cuts on Tuesday afternoon (12 May), just hours after the government extended its job retention, or furlough, scheme.
CityFlyer operates British Airways branded flights from its London City and Edinburgh airport bases, and flies to several other UK airports.
According to Balpa, CityFlyer has identified 72 potential pilot redundancies out of a total of 248, with the axe mainly falling at Edinburgh airport.
The union added it had concerns over the entire CityFlyer operation after BA last month announced it was looking to cut up to 12,000 jobs across its entire business.
Balpa general secretary Brian Strutton said: “CityFlyer had been a successful part of BA so this is yet more shocking and devastating news.
"While the chancellor fanfares his job retention scheme, the aviation industry continues to haemorrhage jobs.
“The government is making this crisis worse for aviation by imposing restrictions on flying and forcing airlines into a death spiral.
"Balpa will fight for every job in CityFlyer at London City and Edinburgh airports which rely on this important and efficient airline.”
It comes after Willie Walsh, chief executive of BA parent IAG, on Monday (11 May) cast doubt on the future of BA’s operations at London City.
He told the government’s transport committee the airport had been more severely affected by the coronavirus crisis owing to the volume of business travel passengers it accommodates.
“Our future there will be something we will consider with the elected representatives of the BA CityFlyer operation," said Walsh.
A BA spokesperson declined to comment further on the CityFlyer proposals after entering into consultation with its unions.