The problems were centred on MUSE software made by Collins Aerospace, which provides systems for several airlines at airports globally, airports said.
RTX, Collins Aerospace's parent company, said it was aware of a "cyber-related disruption" to the software at selected airports, without naming them.
Heathrow Airport said it was among those affected.
Brussels Airport and Berlin Airport were also affected, they said separately.
Brussels Airport said the incident occurred on Friday night.
"There was a cyber attack on Friday night 19 September against the service provider for the check-in and boarding systems affecting several European airports including Brussels Airport," it said in a statement.
Hours later, Dublin Airport said it was also facing minor effects from the issue, along with Cork Airport, Ireland's second biggest after Dublin.
"The impact is limited to electronic customer check-in and baggage drop and can be mitigated with manual check-in operations," RTX said in an emailed statement, adding that it was working to fix the issue as quickly as possible.
It did not give any information on who might be behind the attack.
At Heathrow, Berlin and Brussels, 29 flight departures and arrivals had been cancelled as of midday on Saturday, aviation data provider Cirium said.
In total, 651 departures were scheduled from Heathrow, 228 from Brussels and 226 from Berlin on Saturday.
Officials in Brussels said there had been four flight diversions, as well as "delays on most of the departing flights".
Brussels Airport said it had asked airlines to cancel half of their scheduled departing flights on Sunday to avoid long queues and late cancellations, signalling that the disruption would continue through the weekend.
A European Commission spokesperson said there were currently no indications of a "widespread or severe attack" and that the origin of the incident was still under investigation.
These kinds of sweeping outages are typically the result either of ransomware attacks, where online extortionists paralyse corporate networks in the hope of payment, or deliberate digital sabotage.
Rafe Pilling, director of threat intelligence at cybersecurity company Sophos, said the impact of the incident highlighted "the fragile and interdependent nature of the digital ecosystem underpinning air travel".
"We've seen huge impact across retail and currently automotive in the UK this year," he said.
"The threat is significant and very real."
Passengers with a flight scheduled for Saturday were advised by the affected airports to confirm their travel with airlines before heading to the airport.
Berlin Airport said on its website there were longer waiting times at check-in and it was working on a quick solution.
Frankfurt Airport, Germany's largest, was not affected, a spokesperson said.
"I arrived here at the airport station at about quarter past nine, and we haven't been told anything except that there was a technical fault," Kim Reisen told Reuters at Berlin Airport.
"Of course, online you can read that it was probably a cyber attack, and now we're waiting here to see what happens."
Arguments broke out between passengers waiting in long queues at Heathrow Airport's Terminal 4 on Saturday evening.
Amid lengthy lines at the check-in area, one woman shouted at another woman: "Get out and stop pushing. Everyone is tired, it's not an excuse."
Other passengers were in heated conversations with airport staff, as frustration levels rose at the transport hub because of the delays.
with AP and PA
