Minister of Basic Education Angie Motshekga said that, under strict social distancing rules, other grades would be able to attend lessons in smaller schools with fewer than 150 pupils.
Bigger schools will open for other grades at a later date.
South Africa, the African nation worst hit by COVID-19 with 16,433 infections and 286 deaths, began a phased easing of its lockdown at the start of May.
All teachers are expected to return to work from May 25 and the revised school calendar will be published soon, the minister said, adding that school sports would not be permitted.
"When class is dismissed, learners must go home," she said.
Some parents and teachers have raised concerns about risks to their health and that of their children, urging the department to make sure that schools are properly supplied with personal protective equipment, sanitisers and temperature scanners.
The closure of schools halted a national feeding programme providing meals to 9 million extremely poor children, which Motshekga would resume on June 1.