The BBC said the decision was due to declining listener numbers on medium wave, a preference for the audio quality of other services and maintenance costs were high as the equipment had reached the end of its life.
It said for those listeners who listen to the States of Guernsey Assembly meetings on medium wave, it was currently committed to broadcasting this service on DAB.
The BBC said there were no plans to remove BBC Local Radio from FM.
BBC Radio Jersey is available on 88.8 FM, digital radio as BBC Radio Jersey, Freeview channel 711, Freely channel 712 and online on BBC Sounds or via smart speaker.
BBC Radio Guernsey is available on 93.2 FM covering Guernsey and on 99.0 FM covering Alderney, digital radio as BBC Guernsey and BBC Guernsey Xtra, Freeview channel 721, Freely channel 709 and online on BBC Sounds or via smart speaker.