Children in nurseries and primaries one to three are due back in Scottish schools from Monday, along with some senior secondary pupils who need to do practical work for qualifications.
Mr Swinney said the return of younger pupils should not be a cause for adults to relax restrictions.
He acknowledged that the government had little “headroom” regarding the R number – the rate at which the virus grows.
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Mr Swinney told BBC 1 Scotland’s Sunday Show: “I know this can be quite controversial at times but adults making sure they follow all of the physical distancing requirements at the school gate, or the mask-wearing requirements, is critical to make sure that the return of young children – who are much less susceptible to transmitting the virus – is not in some way undermined by the fact that there is essentially parental transmission.”
He added: “We’ve all got to play a part, not just the school environment but the whole surrounding environment of society, to make sure that we do all that we can to suppress the virus, because we don’t actually have an awful lot of headroom between where the R level is just now – somewhere between 0.7 and 0.9 – and 1, where, obviously, the virus begins to spread exponentially.”
Mr Swinney said ministers would be monitoring data carefully when the initial cohort of pupils returns before deciding on whether others could go back to class.
The UK government has said it hopes to open all schools in England on 8 March , depending on falling infection rates.
Asked about this, Mr Swinney responded: “What we will do in Scotland is work to get all pupils back to face-to-face learning at the earliest possible opportunity.
“Safety is absolutely paramount in doing that. That’s why we’ve taken the careful decisions we’ve taken for tomorrow.”