Gavin Williamson said a return to school will be "compulsory" and families may face financial penalties if they keep their children at home - unless there is a "good reason" for the absence.
A detailed plan on how the Government will ensure that all children in England are back in the classroom in the autumn will be set out by the end of this week, the minister said.
His remarks came as Labour leader Sir Keir Starmer accused the Government of being "asleep at the wheel" on the issue of reopening schools, adding that there has been a "lack of planning".
Speaking on Sky News, he said: "If you could put up Nightingale hospitals - a good thing to do - you can certainly put up temporary classrooms, you can certainly take over libraries, community centres."
Mr Williamson said the Government is still consulting on how to return all pupils to the classroom in the autumn, but that advice for schools on reopening will be unveiled this week.
He also confirmed on Monday that families could be fined if they do not send their children back in September.
He told LBC: "It is going to be compulsory for children to return back to school unless there's a very good reason, or a local spike where there have had to be local lockdowns.
"We do have to get back into compulsory education as part of that, obviously fines sit alongside that.
"Unless there is a good reason for the absence then we will be looking at the fact that we would be imposing fines on families if they are not sending their children back."
Some children began returning to school at the beginning of this month - but, ahead of the phased reopening, the Government confirmed that parents who do not feel safe sending their children back to school would not face fines.
The latest Government figures show that around a third (34%) of all Year 6 children attended school on June 18, up from 26% on June 11.
Attendance was around a quarter (26%) in Year 1, up from a fifth the previous week, and 29% in Reception, up from 22% on June 11, the figures show.
Speaking on Monday, Boris Johnson said the fact that more pupils are not back at school yet is a source of "deep frustration" for him.
The Prime Minister told Times Radio that teaching unions and councils should be saying "loud and clear" that schools are safe.
Asked if there will be a detailed plan for a return to school in September this week, Mr Williamson told BBC Radio 4's Today programme: "There will be."
He said: "We're going to take the opportunity to spell out exactly as to how we will see a full return for all children back into school before the end of this week.
"As I'm sure you'll understand and appreciate at the moment, we're consulting and talking with different people, whether it's headteachers, whether it's unions, whether it's representative bodies."
Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), has called for a "period of grace" before fining parents if they refuse to send their children back to school when they fully reopen.
He said: "We don't think that it is the right approach to fine parents for the non-attendance of children as soon as schools fully reopen in September, and the Government should not expect schools to take this action.
"There will be many frightened and anxious parents out there, and this is very much a case of building confidence that it is safe to return, rather than forcing the issue through the use of fines.
"The Government must show a greater understanding of the realities of the situation, and we would recommend that there is a period of grace while normal patterns resume."