It's not yet clear if they both had the Omicron variant.
"The situation is pretty concerning," Mathivha told the South African Broadcasting Corporation (SABC).
"Because this is not something that we had observed with the first, second and third wave.
" … In the past, the children used to get a Covid infection … and it wouldn't really put them down, it wouldn't really send them to hospital in big number to be admitted.
"We are now seeing them [children] coming in with moderate to severe symptoms needing supplemental oxygen, needing supportive therapy, needing to stay in hospital for quite a number of days.
"But what really broke my heart yesterday was a 15-year-old previously well child, no illness. Two day history of fever, comes into the hospital, tests positive for Covid and literally deteriorates in front of our eyes and nothing, no supportive therapy that we could do could help him.
"And we lost that patient … this is the first incident [here] of a child who had no comorbidities and nothing existing before who has passed from Covid that I am aware of."
She warned the hospital may soon not be able to accommodate any more children.
"This is going to be a major problem for us. Our hospitals were not built to house a lot of children. Because naturally children do not get that sick in multitude.
"We will not be able to accommodate them, and I'm not saying this to make people panic," Mathivha said.
"I am saying this to say, all these preventive measures we take to interrupt transmission of Covid let them be applied to the children as well."
Children 12 years and under are not yet eligible for vaccination in the country.
South Africa is currently in the fourth wave of the pandemic, due to Omicron.
On Saturday, the South African Government said the Omicron variant of Covid-19 is disproportionately affecting children under 5 as experts rubbish the notion that the latest strain is "mild".
Government adviser Waasila Jassat told reporters in the Johannesburg area, where the virus is spreading widely, there has been "quite a sharp increase" in hospital admissions "across all age groups but particularly in the under 5".
"The incidence in those under 5 is now second highest, second only to those over 60," she said.
The Daily Beast reported epidemiologist Michelle Groome told the virtual press conference in South Africa that seven-day average for cases in one badly-affected province had jumped from 332 to more than 4800 in three days.
And on Friday it was reported that children under the age of 2 now make up 10 per cent of hospital admissions in South Africa's Omicron ground zero.
While the new variant was first detected in Botswana, South Africa has emerged as the strain's epicentre, with the city of Tshwane in the Gauteng province one of the worst affected regions.
According to an analysis by South Africa's National Institute for Communicable Diseases (NICD), there has been a recent surge in Covid hospital admissions among toddlers.
Speaking during a media briefing by the Department of Health this week, NICD's Dr Waasila Jassat said young children seemed to be "more at risk", although it was not yet clear if the surge in admissions was linked to Omicron.
"When you look at the numbers of admissions by age, what we normally see is a large number of admissions in older people.
"But in this early resurgence in Tshwane, we are seeing most admissions in the 0-2 age group. And we are seeing a large number of admissions in the middle ages, sort of around 28 to 38."
Jassat said the trend could be because children under 12 were not vaccinated, and also because parents were more concerned about the new variant, and therefore more likely to take their children to hospital at the first signs of illness.
"The very young children have an immature immune system and they are also not vaccinated, so they are more at risk."
