The Met Office says it will make for difficult driving conditions and could cause travel delays in some areas.
It will last from 4.20am until 10.30am, with delays to bus and train services being possible.
A spokesman for the Met Office said: "Areas of freezing fog have formed and will be dense at times and slow to clear from some places today.
"Visibility as low as 50 to 100 metres is likely in a few areas and some untreated surfaces could turn icy, this combination resulting in potentially difficult driving conditions.
"Tonight will be less chilly than previous nights, but slight frost is possible during the evening under clear spells.
"The rest of the week will see sunny spells and largely dry on Thursday and Friday following chilly starts and possible fog patches. Cloud and patchy rain arriving for Saturday."