The two airlines are being investigated for potentially breaching consumer law.
The CMA is concerned they failed to offer refunds for flights that customers could not legally take due to Covid lockdowns
The watchdog launched a probe into the airlines sector in December last year.
The Competition and Markets Authority said the investigation relates to flights that were not cancelled but that customers could not take because it was unlawful for people in the UK to travel for non-essential reasons - for example during the second lockdown in England in November.
The CMA's chief executive, Andrea Coscelli, said: 'Customers booked these flights in good faith and were legally unable to take them due to circumstances entirely outside of their control.
We believe these people should have been offered their money back.
The move comes after the watchdog launched a probe into the airlines sector in December last year,
following reports that during the Covid-19 pandemic, customers were denied refunds while unable to fly and were instead offered vouchers or the option to rebook flights.
During periods of lockdown across the UK, British Airways offered vouchers or rebooking to affected customers, while Ryanair only provided the option to rebook. But legally, customers are entitled to a cash refund within 14 days.