Mr Swinney also confirmed that face coverings will not be a mandatory requirement in communal areas in schools after April 18.
Nicola Sturgeon said in January the latest a decision could be made on school assessments was the end of March, although it was her “firm intention” for the diet to go ahead as planned.
“The exam diet will go ahead, and that’s the approach that has been taken,” Mr Swinney said in response to a question from Conservative MSP Murdo Fraser.
On March 22, Scottish Government figures showed 27,015 pupils were not in schools as a result of Covid-19.
Some 5,815 staff were absent on the same day.
The new BA.2 strain of the Omicron variant has contributed to a spike in cases, which the First Minister said on Wednesday appeared to be levelling off.
When asked what support could be offered to pupils forced to miss exams because of the virus, Mr Swinney, who is himself self-isolating after testing positive, said: “There are routine arrangements in place to address the implications of that on a pupil by pupil basis and no pupil will be disadvantaged by those arrangements.”
He added: “The Scottish Qualifications Authority will work with individual schools to make sure that no pupil is disadvantaged in that respect.”
In response to another question from Mr Fraser, Mr Swinney said face coverings will not be required in communal areas of schools after the Easter holidays.
The legal requirement to wear face coverings will be converted to guidance for weddings, funerals and places of worship from Monday, and for other public settings including shops, transport and hospitality from April 18.
There had been some confusion over whether this would apply to schools, as a Scottish Government spokesperson said on Wednesday that it would not.
But asked to clarify, Mr Swinney said: "The position, I understand, is that masks will not be required in communal areas as an obligation from April 18, but that wearing them will be recommended as something that will be beneficial for maintaining some protection.”