He echoed the announced from the Prime Minister, Boris Johnson, that people should remain indoors except for shopping for basic necessities, daily exercise, any medical need and travelling to and from essential work.
AMs will debate whether to give their consent to the coronavirus law, which is expected to be passed swiftly by the UK Parliament in Westminster.
The regular first minister’s questions session will not take place, although Mr Drakeford will give a statement on coronavirus.
Six government AMs, three Conservatives, two Plaid AMs, and one Brexit Party AM are expected to attend. It is not clear if any independents will take part.
The UK government has worked on the coronvirus legislation alongside the Welsh, Scottish and Northern Ireland administrations.
It provides sweeping measures, for up to two years, to help UK authorities tackle the coronavirus outbreak. It will need to be reviewed by Parliament every six months.
Although it is UK legislation, which was examined by the House of Commons on Monday and will be considered by the Lords on Tuesday and Wednesday, its provisions for Wales mean AMs must give their formal permission through a legislative consent motion.
Vaughan Gething, health minister, will also address the Senedd in a shorter Plenary session.
The session will begin at the earlier than usual time of 10:00 GMT.