This comes after the government reopened schools for Cambridge examination classes on September 14. Zimbabwe Schools Examination Council (Zimsec) examination classes will reopen on September 28.
The two minors, whose identities have not been given, are the first and second applicants represented by a children's organisation, Care at the Core of Humanity (Catch).
Education minister Cain Mathema, Public Service minister Paul Mavima, Finance minister Mthuli Ncube and Zimbabwe Human Rights Commission are cited as respondents in the application filed before the High Court.
One of the minors is due to sit for Zimsec Grade 7 examinations and wants the government to assess children in vulnerable communities who have not been able to access online and electronic lessons.
In an affidavit, their father argued that children in better-off economic circumstances had benefited from online and electronic lessons which he could not afford.
He said as a subsistence farmer in remote Nenguwo Village in Manicaland and a sole breadwinner to his family and other dependents from his extended family, he could not afford a radio.
"My children have not been able to attend any of these lessons because of their penurious circumstances. That is to say, the family does not own a radio set. We cannot afford to buy or maintain one since a radio would need a constant power supply from either batteries or solar power," he said.
"I am aware that the issues raised in this application affect many thousands of children in the most remote rural areas of Zimbabwe. May this fact not be lost to the court which is the upper guardian of all children in Zimbabwe."
He said failure by the government to put in place measures that ensured every child continued learning during the lockdown period was a denial of their right to education as enshrined in the Constitution.
"The respondents must be aware that there are children in this country who live in circumstances of dire poverty and marginalisation and yet they have not acknowledged this in the measures the government has adopted to continue to provide education services during the lockdown crisis," he said.
"Indeed, even if I were to afford a radio for my children, the area I stay in is rugged and mountainous and receives radio waves only erratically."
He argued that the government had defied the right to equality and non-discrimination.
"The first applicant has been treated in a discriminatory manner because other children are accorded directly or indirectly the privilege and advantage of radio lessons which she has not been accorded due to her economic and social status."