The US Department of Transportation said the airline had not provided "timely refunds to passengers" for abandoned or rescheduled flights to and from the country.
It said it had received more than 1,200 complaints about the airline.
BA rejected the claims, saying it had "acted lawfully at all times".
According to the transport department, from March to November 2020, BA's website instructed consumers to contact the carrier by phone to discuss refund options, including for flights the carrier had cancelled or significantly changed.
However, consumers were unable to get through to customer service agents when calling the carrier for several months during this period because BA failed to maintain adequate functionality of its customer service phone lines , it said.
"There was also no way to submit a refund request through the carrier's website during this period," the department said.
It added that from March to November 2020, misleading information on BA's website had led consumers to inadvertently request travel vouchers instead of refunds.
It said that along with the 1,200 complaints received by the department, BA had received thousands more complaints and refund requests directly from consumers.
The department said the failures had "caused significant challenges and delays in thousands of consumers receiving required refunds".
It added that the fine established a "strong deterrent to future similar unlawful practices".
BA will be credited $550,000 towards the penalty because it paid more than $40m in refunds to customers with non-refundable tickets in 2020 and 2021.
The airline said: "We're very sorry that at the height of the unprecedented pandemic - when we were unfortunately forced to cancel thousands of flights and close some call centres due to government restrictions - our customers experienced slightly longer wait times to reach customer service teams.
"During this period, we acted lawfully at all times and offered customers the flexibility of rebooking travel on different dates, or claiming a refund if their flights were cancelled.
"To date, we have issued more than five million refunds since the start of the pandemic."
BBC