The airport said it was experiencing a knock-on effect from poor weather on Friday but also from fog which is causing problems in south-east England.
Some earlier flights were diverted to Bristol with others delayed by up to 90 minutes.
The disruption was set to continue through the day and there have also been further problems on the railway.
Network Rail said as well as delays caused by overrunning engineering works, Arriva Trains Wales Services had a shortage of train crew which was causing disruption.
Services running through Cardiff have been affected and a replacement bus service for Arriva Trains Wales services between Bridgend and Cardiff Central is in place.
A spokeswoman from Cardiff Airport said: "Due to fog across the UK and Europe there is disruption to flights operating to and from Cardiff Airport today.
"Passengers are advised to contact their airline for updates."
Fog has caused flights in and out of Cardiff Airport to be delayed or diverted.