Supergrass, The Feeling and Manic Street Preachers were all scheduled to play at the event later this month.
It was planned to be held at Singleton Park in Swansea from 13-15 July, with 30,000 visitors each day.
Straight Music released a statement, explaining: "This has been a hard, but well considered decision and we believe it is the best one for all concerned."
They added: "Due to the bad weather, we have been delayed in putting the infrastructure in place and it is a big concern that the weather conditions will hugely dampen the experience we want to give all our festival goers.
"Postponing the festival will mean that we can give everyone the Fflam festival experience they deserve, bands, organisers and festival goers alike."
Festival organisers confirmed that full refunds would be available from the point of purchase but promised that the event will go ahead at a later date.