The warning is in place from 3pm on Wednesday until 8pm on Monday, June 22.
A yellow alert means that minor impacts are likely across health and social care services.
A heat health alert has been issued for Norfolk (Image: James Bass)
It also warns of a greater risk to life of vulnerable people, increased potential for indoor environments to become very warm and water‑related incidents may increase, including risks from cold‑water shock and drowning.
The risk score is currently at seven, the lowest of the ratings to trigger a warning.
However, this can change with forecasts.
Met Office meteorologist Honor Criswick said high pressure building across the country will bring warm and humid conditions, with temperatures climbing above the seasonal average in some areas.
Temperatures are set to creep up towards the 30C, with the mercury peaking on Friday.
Crowds at Sea Palling beach during the heatwave over the bank holiday weekend (Image: Mike Page)
Diss in south Norfolk will hit the 30C mark on Friday, while Downham Market will reach 28C and Thetford 29C.
Great Yarmouth will also peak at around 28C on the Friday, while Norwich will hit 29C.
Elsewhere, Sheringham is expected to reach 28C and Attleborough 29C.
“Throughout the week things are heating up in the south and South East,” she said.
“We’ve got high pressure starting to build and there’s a warm plume moving up through continental Europe.
“Whether or not it’ll be a heatwave remains to be seen as there’s still a lot to play for, but things are certainly turning a lot warmer, if not maybe even hot, by the end of the week, although this is mostly confined to the South East.
“Other areas will warm up, but it’s also very humid so they are likely to be cloudy, with rain and showers.”