Eurocontrol, which co-ordinates flights across the continent, said almost 15,000 scheduled trips “could have some delay”.
Contingency plans put in place have reduced the network capacity by another 10%, it said.
The problem is expected to be solved late on Tuesday evening.
Eurocontrol said there had been a failure in its Enhanced Tactical Flow Management System.
The system helps to manage air traffic by comparing demand and capacity of different air traffic control sectors.
Air traffic control itself has not been directly affected, and Eurocontrol said there “are no safety implications arising from this incident”.
“We have never had anything like this before,” a Eurocontrol spokesman told the AFP news agency. On Twitter, the group said that it regrets the inconvenience, but that “safety is our number one priority at all times”.