Gillian Keegan has said she will work with head teachers to make sure schools are open for as many children as possible, but admitted she cannot guarantee there will be no closures.
Some parents have voiced concerns about having to arrange childcare on strike days and the possible financial impact of having to take days off work, according to Mumsnet.
But a spokeswoman from the parenting website said there appeared to be anecdotal evidence of "empathy and understanding" for striking teachers, amid a "crisis" in recruitment and retention.
Rhiannon Evans, head of communications and public affairs at Mumsnet, said: "I think the thing that's really interesting is that although parents are concerned about how it [a strike] will affect their kids' education, if you have a look at the discussions on site, there is a very strong feeling amongst parents that there's obviously a crisis in recruitment and retention with teachers leaving the profession, and that's already having an effect on kids' education."
A thread on concerns about the teacher strikes had more than 46,000 views - making it the third most-viewed thread on the site - on Monday as the ballot results were announced.
Ms Evans said: "Parents are concerned about their children's education. Lots of these kids will have already had their education disrupted by Covid-19 and I think there's a bit of a sense among some parents that they had just sort of settled back into a normal rhythm and obviously strikes will disrupt their education further, even if it's on a much smaller scale.
"The other big concern for parents is, obviously with parents of younger children, if schools are closed then they'll have to take time off work or arrange care, and for some parents that will obviously have a financial impact.
"And we know that in most cases it will be women who bear the brunt of that. We know that it's usually women, it's usually mums, who end up doing the childcare in this kind of situation."
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Nine out of ten teacher members of the National Education Union (NEU) who voted in a ballot backed strike action, while the union said walkouts could affect more than 23,000 schools.
The NEU plans to hold seven days of walkouts in February and March in a dispute over pay - with the first on February 1 coinciding with walkouts by staff at universities, on the rail network and in Whitehall.
Ms Keegan has described the teachers' strike action as "deeply disappointing for children and parents".
Updated guidance from the Department for Education (DfE) suggests agency staff and volunteers could be used to cover classes on strike days, with schools expected to remain open where possible, although remote learning is an option and the most vulnerable pupils are to be given priority.
But Paul Whiteman, general secretary of the National Association of Head Teachers (NAHT), said schools could have to shut during walkouts if "staffing numbers are dangerously low", and branded the guidance "at best naive".