John Swinney MSP was speaking on the BBC's Good Morning Scotland radio programme on Tuesday when he revealed institutions north of the border will be shut until at least that period is over.
Scotland's First Minister, Nicola Sturgeon, previously said she could not "promise" they would be able to reopen before that time.
Mr Swinney said that schools will remain closed for the foreseeable future, which is expected to be until at least the summer break is over.
He added: "What I can say is that for the foreseeable future schools will be closed.
"We have taken no decisions to reopen schools and, as we said back in March, we expect them to be closed until at least the summer break.
"We are seeing the progress that is being made on slowing up the coronavirus just now, but that's on the basis that only one in every 200 children are in schools today.
"The minute we say more people can be in that school, we are acknowledging that the risk of the spread of coronavirus rises and we can't afford to take that risk."
Mr Swinney also responded to concerns the lockdown would worsen the poverty attainment gap.
He told the broadcaster that devices such as laptops would be able to be shared more widely and they could use money to tackle the attainment gap with fewer restrictions.
The deputy first minister said: "What I've said to schools is that they can exercise much greater flexibility over the use of pupil equity funding and the resources that we allocate especially for the Scottish Attainment Challenge."
When asked whether schools could give out devices such as laptops, he added: "Yes they could, or many schools already do that and many schools already provide all young people with devices that enable them to interact with their learning remotely.
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