The RHS issued the advice to prevent the spread of Fuchsia gall mite. Principal entomologist Andrew Halstead said it predicted infestations to "increase significantly in the next few years". The pest cannot be treated by readily available pesticides.
He said: "This is a devastating pest because it destroys the plant's shoot tips and flowers. As this pest becomes more widespread, I anticipate that (the plant's) popularity will go into sharp decline."
Gardeners have been advised to dig up and burn or bury any infected plants and those in neighbouring gardens and to leave a year's gap before replanting.
Mike Clare of Fuchsia specialist Potash Nurseries described the advice as "a bit over the top" and said: "I would have thought that they are going to frighten people away - to start telling people not to buy them or to throw them away is a bit too much."
British Fuchsia Society president Carol Gubler said: "I don't think the nurseries should panic. As long as we are vigilant we should be fine."
Eoin Redahan of the RHS responded: "If this mite takes hold then it is more likely that sales of Fuchsias will be even more drastically affected. We are a little surprised that there has not been a stronger reaction from producers to the news that control and eradication of this pest within private gardens has been abandoned."