A small number of people working in education have tested positive for coronavirus since lockdown started and the majority of schools closed in March.
The latest figures, which are up to May 31, have shown that of the 440 education workers tested, 24 have tested positive and 416 have tested negative.
Since schools shut on March 20 children have been learning from home, while the children of key workers and those deemed vulnerable can go in for childcare at hub schools. Around 6,000 are currently in hub schools.
Residential and special schools have also been operating during the lockdown and are represented in the figures.
The Welsh Government announcement for a phased re-opening of schools on June 29 has been met with a mixed response, with many parents and union raising concerns.
Wales' chief medical officer has said the decision to re-open schools on June 29 was not his "preferred option".
Speaking at the daily press conference in Cathays Park, Dr Frank Atherton said the decision made by the Welsh Government was the "second best option".
She added that a quarter of schools in Wales have been open during this period, and that they had been able to successfully mange the risks in that time.
Ms Williams told BBC Radio Wales listeners on Thursday: "We have been testing teachers and support staff working in our hubs and the vast majority of those tests have come back negative.
"We have had a small amount of positive tests and, of course, it is impossible to know whether that member of staff contracted the virus while being at work, or whether they contracted that virus whilst being out in their community doing their shopping, for instance.
"What is really important is that teachers and everybody working in the hubs will be priorities for our new antibody testing regime so we can better understand the virus. I acknowledge there are risks involved in going back, but there are risks in not doing so."
The education minister also said it was about "balancing risks".
She added: "It is about balancing risks. Balancing the risk presented by the virus, but also balancing the risks about what it means to children, the majority of whom, if we don't go back until September, will have spent six months without stepping inside a classroom.
"We have learnt lessons, we have amended our guidance and always looked at how to make it better. It would be wrong of me to suggest to anybody that I can make an environment 100% risk free. What I can do is ensure that the decisions that we are making mitigate the risks as much as possible.
"We wouldn't be asking people to move their children into somewhere we didn't think was safe."
The testing figures also show that 150 emergency services workers have tested positive, while 720 have tested negative.
