Flights to and from the UK's two busiest airports, Heathrow and Gatwick, appear to be among those affected.
By 9am on Thursday, 45 flights due to land at Heathrow had been delayed by more than 45 minutes.
The worst affected was Flight BA170 from Pittsburgh, in the US, which was more than 12 hours behind schedule.
A spokeswoman for the airline said: "Our teams are working hard to resolve a technical issue which is affecting some of our flights, and we have rebooked customers on to alternative flights and offered hotel accommodation where they have been unable to continue their journeys last night.
"We are very sorry for the disruption to their travel plans.
"We plan to operate a full flight schedule today."
Customers were urged to check ba.com for latest flight information and ensure their contact details are up to date on their booking.
The airline has suffered a series of systems failures in recent months.
In August, an IT glitch caused the cancellation of more than 100 flights and disrupted the travel plans of tens of thousands of passengers.
Rory Boland, editor of Which? Travel magazine, said: "This is the latest in a long line of British Airways technical glitches causing delays and cancellations and yet again it's thousands of passengers who are paying the price - left tired, frustrated and with a lack of information and assistance from the airline.
"BA must do the right thing and reroute passengers as quickly as possible, using other airlines where necessary, as well as informing customers facing disruption about their entitlement to compensation."