The closure forms part of the BBC’s decision to end medium wave transmissions in five regions, including Cumbria, Derby, Gloucestershire, and Somerset, by the end of November.
The BBC said the change reflects shifting listener habits and is not a reduction in its commitment to local radio.
A spokesman said: “The closure of these final MW services is not a change in our commitment to local radio.
“It is a change in how that service is delivered, reflecting how audiences already choose to listen today.”
Medium wave has been in use since 1972, but with audiences increasingly turning to newer platforms, the BBC said maintaining the service had become “difficult to justify”.
Listeners will still be able to tune in to BBC Radio Norfolk and other affected stations via FM, DAB digital radio, BBC Sounds, smart speakers, and the BBC website.
The BBC has been broadcasting on-air messages directing listeners to alternative platforms.